Fuzzing -- From Alchemy to a Science

Talk at Passau University

Transcript

1. Fuzzing Rahul Gopinath
2. Fuzzing from Alchemy Rahul Gopinath
3. Fuzzing from Alchemy Rahul Gopinath
4. Fuzzing from Alchemy to Science Rahul Gopinath
5. Fuzzing from Alchemy to Science Rahul Gopinath
7. 4 The story begins 2500 years ago. 500 BC
8. 4 Vedic Sanskrit 500 BC
9. 4 Vedic Sanskrit Classical Sanskrit 500 BC
10. 5 500 BC Vedic Sanskrit Classical Sanskrit
11. 5 500 BC Aṣṭādhyāyī Dakṣiputra Pāṇini Vedic Sanskrit Classical Sanskrit
12. 5 500 BC Aṣṭādhyāyī Dakṣiputra Pāṇini Ad hoc rules Formal specification Vedic Sanskrit Classical Sanskrit
14. 6 2500 years later.... 2021 CE The world is governed by software
15. 6 2500 years later.... 2021 CE We have a crisis The world is governed by software
16. 7 Debian 5 ~ 70 million lines Smart cars ~ 100 million lines Google is ~ 2 Billion lines 5 M 10 M 15 M 20 M 25 M 30 M 35 M (Source: Wikipedia) #Linux Kernel Size in Millions of Lines of Code Linux Releases Growth in software complexity
17. 7 Debian 5 ~ 70 million lines Smart cars ~ 100 million lines Google is ~ 2 Billion lines 1994 1996 1.0.0 2.0.0 2.1.0 2.2.0 2.4.0 2.6.0 2003 2011 3.0 2015 4.0 2019 5.0 2019 5.7 2001 5 M 10 M 15 M 20 M 25 M 30 M 35 M (Source: Wikipedia) #Linux Kernel Size in Millions of Lines of Code Linux Releases Growth in software complexity
18. 8 Growth in vulnerabilities #Vulnerabilities Year 16k 14k 12k 10k 8k 6k 4k 2k (Source: NIST)
19. 8 Growth in vulnerabilities #Vulnerabilities Year 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 16k 14k 12k 10k 8k 6k 4k 2k (Source: NIST)
20. Fuzzing Program Trash deck technique: 1950s - Gerald Weinberg
21. Fuzzing Program Trash deck technique: 1950s - Gerald Weinberg
22. Fuzzing Crash? Program Trash deck technique: 1950s - Gerald Weinberg
23. 10 Fuzzing Random Inputs Program Automatic Checks
24. 10 Fuzzing • Memory Bounds Violation • Privilege Escalation • Safety Violations • Metamorphic Relations • Differential Execution Random Inputs Program Automatic Checks
25. 11 Random Fuzzing Program
26. 11 Random Fuzzing $ ./fuzz [;x1-GPZ+wcckc];,N9J+?#6^6\e?]9lu
 2_%'4GX"0VUB[E/r ~fApu6b8<{%siq8Z
 h.6{V,hr?;{Ti.r3PIxMMMv6{xS^+'Hq!
 AxB"YXRS@!Kd6;wtAMefFWM(`|J_<1~o}
 z3K(CCzRH JIIvHz>_*.\>JrlU32~eGP?
 lR=bF3+;y$3lodQ<B89!5"W2fK*vE7v{'
 )KC-i,c{<[~m!]o;{.'}Gj\(X}EtYetrp
 bY@aGZ1{P!AZU7x#4(Rtn!q4nCwqol^y6
 }0|Ko=*JK~;zMKV=9Nai:wxu{J&UV#HaU
 )*BiC<),`+t*gka<W=Z.%T5WGHZpI30D<
 Pq>&]BS6R&j?#tP7iaV}-}`\?[_[Z^LBM
 PG-FKj'\xwuZ1=Q`^`5,$N$Q@[!CuRzJ2
 D|vBy!^zkhdf3C5PAkR?V((-%><hn|3='
 i2Qx]D$qs4O`1@fevnG'2\11Vf3piU37@
 5:dfd45*(7^%5ap\zIyl"'f,$ee,J4Gw:
 cgNKLie3nx9(`efSlg6#[K"@WjhZ}r[Sc
 un&sBCS,T[/3]KAeEnQ7lU)3Pn,0)G/6N
 -wyzj/MTd#A;r*(ds./df3r8Odaf?/<#r Program ✘
27. $ ./fuzz -int | program 634111569742810193727424069509 741355925061499451162464719526 615957331924826555590537407605 181400079803446874252046374716 740973770255348279425601333144 152724057932073828569041216191 099859446496509919024810271242 622974988671421938012464630138 735355134599327240920259675263 574528613057084231370741920902 794677842164654990353575580453 777282305855352378119038096476 699871306655084953377039862387 924957554389878352934547664240 082431556093837288597262675598 630851919061829885048834738832 677022429414980917053939970795 722006987916088650168665471731 yes 12 Random Fuzzing def is_prime(n: int) -> bool: """Primality test using 6k+-1 optimization.""" if n <= 3: return n > 1 if n % 2 == 0 or n % 3 == 0: return False i = 5 while i ** 2 <= n: if n % i == 0 or n % (i + 2) == 0: return False i += 6 return True def main(): num = stdin.read() print(num, is_prime(num))
28. $ ./fuzz -int | program 634111569742810193727424069509 741355925061499451162464719526 615957331924826555590537407605 181400079803446874252046374716 740973770255348279425601333144 152724057932073828569041216191 099859446496509919024810271242 622974988671421938012464630138 735355134599327240920259675263 574528613057084231370741920902 794677842164654990353575580453 777282305855352378119038096476 699871306655084953377039862387 924957554389878352934547664240 082431556093837288597262675598 630851919061829885048834738832 677022429414980917053939970795 722006987916088650168665471731 yes 12 Random Fuzzing def is_prime(n: int) -> bool: """Primality test using 6k+-1 optimization.""" if n <= 3: return n > 1 if n % 2 == 0 or n % 3 == 0: return False i = 5 while i ** 2 <= n: if n % i == 0 or n % (i + 2) == 0: return False i += 6 return True def main(): num = stdin.read() print(num, is_prime(num)) Weak point: unequal divisions in input space Input space n > 3 n <= 3
29. 13 Advanced Fuzzing: Instrumentation
30. 14 Advanced Fuzzing: Instrumentation def triangle(a, b, c): if a == b: if b == c: return Equilateral else: return Isosceles else: if b == c: return Isosceles else: if a == c: return Isosceles else: return Scalene def triangle(a, b, c): if a == b: if b == c: return Equilateral else: return Isosceles else: if b == c: return Isosceles else: if a == c: return Isosceles else: return Scalene
31. 14 Advanced Fuzzing: Instrumentation def triangle(a, b, c): __probe_enter() if a == b: __probe_1() if b == c: __probe_2() return Equilateral else: __probe_3() return Isosceles else: __probe_4() if b == c: __probe_5() return Isosceles else: __probe_6() if a == c: __probe_7() return Isosceles else: __probe_8() return Scalene def triangle(a, b, c): if a == b: if b == c: return Equilateral else: return Isosceles else: if b == c: return Isosceles else: if a == c: return Isosceles else: return Scalene
32. 15 Instrumentation Based Fuzzing def triangle(a, b, c): if a == b: if b == c: return Equilateral else: return Isosceles else: if b == c: return Isosceles else: if a == c: return Isosceles else: return Scalene
33. 15 Instrumentation Based Fuzzing def triangle(a, b, c): if a == b: if b == c: return Equilateral else: return Isosceles else: if b == c: return Isosceles else: if a == c: return Isosceles else: return Scalene triangle (1,1,1)
34. 16 Instrumentation Based Fuzzing def triangle(a, b, c): if a == b: if b == c: return Equilateral else: return Isosceles else: if b == c: return Isosceles else: if a == c: return Isosceles else: return Scalene
35. 16 Instrumentation Based Fuzzing def triangle(a, b, c): if a == b: if b == c: return Equilateral else: return Isosceles else: if b == c: return Isosceles else: if a == c: return Isosceles else: return Scalene triangle (1,1,2)
36. 17 Instrumentation Guided Fuzzing • Coverage Guided • Solver Directed
37. 18 Coverage Guided Fuzzing • Randomly generate inputs • Choose seeds with new coverage
38. 18 Coverage Guided Fuzzing • Randomly generate inputs • Choose seeds with new coverage AFL
39. 19 Coverage Guided Fuzzing • Randomly generate inputs • Choose seeds with new coverage AFL First Release: 2013 AFL Trophy Case
40. 20 Coverage Guided Fuzzing • Randomly generate inputs • Choose seeds with new coverage AFL Pulling JPEGs out of thin air https://lcamtuf.blogspot.com/2014/11/pulling-jpegs-out-of-thin-air.html Valid JPEG in 6 hours in an 8 core machine!
41. 21 Coverage Guided Fuzzing • Randomly generate inputs • Choose seeds with new coverage AFL static int is_reserved_word_token(const char *s, int len) { const char *reserved[] = { "break", "case", "catch", "continue", "debugger", "default", "delete", "do", "else", "false", "finally", "for", "function", "if", "in", "instanceof", "new", "null", "return", "switch", "this", "throw", "true", "try", "typeof", "var", "void", "while", "with", "let", "undefined", ((void *)0)}; int i; if (!mjs_is_alpha(s[0])) return 0; for (i = 0; reserved[i] != ((void *)0); i++) { if (len == (int)strlen(reserved[i]) && strncmp(s, reserved[i], len) == 0) return i + 1; } return 0; }
42. 21 Coverage Guided Fuzzing • Randomly generate inputs • Choose seeds with new coverage AFL static int is_reserved_word_token(const char *s, int len) { const char *reserved[] = { "break", "case", "catch", "continue", "debugger", "default", "delete", "do", "else", "false", "finally", "for", "function", "if", "in", "instanceof", "new", "null", "return", "switch", "this", "throw", "true", "try", "typeof", "var", "void", "while", "with", "let", "undefined", ((void *)0)}; int i; if (!mjs_is_alpha(s[0])) return 0; for (i = 0; reserved[i] != ((void *)0); i++) { if (len == (int)strlen(reserved[i]) && strncmp(s, reserved[i], len) == 0) return i + 1; } return 0; } Weak point: Magic bytes
43. 22 Coverage Guided Fuzzing • Randomly generate inputs • Choose seeds with new coverage
44. 22 Coverage Guided Fuzzing • Randomly generate inputs • Choose seeds with new coverage
45. 23 Solver Directed Fuzzing • Collect path constraints • Solve negated constraints for new inputs
46. 23 Solver Directed Fuzzing • Collect path constraints • Solve negated constraints for new inputs (a == b) (b == c)
47. 23 Solver Directed Fuzzing • Collect path constraints • Solve negated constraints for new inputs (a == b) (b == c) (b != c)
48. 23 Solver Directed Fuzzing • Collect path constraints • Solve negated constraints for new inputs (a == b) (b == c) (b != c) triangle(1,2,1)
49. 23 Solver Directed Fuzzing • Collect path constraints • Solve negated constraints for new inputs (a == b) (b == c) (b != c) triangle(1,2,1)
50. 24 Solver Directed Fuzzing • Collect path constraints • Solve constraints for new inputs void next_sym() { while(1) { switch (ch){ case '{': next_ch(); sym = LBRA; return; case '}': next_ch(); sym = RBRA; return; case '(': next_ch(); sym = LPAR; return; case ')': next_ch(); sym = RPAR; return; case '+': next_ch(); sym = PLUS; return; case '-': next_ch(); sym = MINUS; return; case '<': next_ch(); sym = LESS; return; case ';': next_ch(); sym = SEMI; return; case '=': next_ch(); sym = EQUAL; return; default: if (ch >= '0' && ch <= '9') { int_val = 0; /* missing overflow check */ while (ch >= '0' && ch <= '9') { int_val = int_val*10 + (ch - '0'); next_ch(); } sym = INT; } else if (ch >= 'a' && ch <= 'z') { int i = 0; /* missing overflow check */ while ((ch >= 'a' && ch <= 'z') || ch == '_'){ id_name[i++] = ch; next_ch(); } id_name[i] = '\0'; sym = 0; while (words[sym] != NULL && strcmp(words[sym], id_name) != 0) sym++; if (words[sym] == NULL) if (id_name[1] == '\0') sym = ID; else syntax_error(); } else syntax_error(); return; }
51. 24 Solver Directed Fuzzing • Collect path constraints • Solve constraints for new inputs void next_sym() { while(1) { switch (ch){ case '{': next_ch(); sym = LBRA; return; case '}': next_ch(); sym = RBRA; return; case '(': next_ch(); sym = LPAR; return; case ')': next_ch(); sym = RPAR; return; case '+': next_ch(); sym = PLUS; return; case '-': next_ch(); sym = MINUS; return; case '<': next_ch(); sym = LESS; return; case ';': next_ch(); sym = SEMI; return; case '=': next_ch(); sym = EQUAL; return; default: if (ch >= '0' && ch <= '9') { int_val = 0; /* missing overflow check */ while (ch >= '0' && ch <= '9') { int_val = int_val*10 + (ch - '0'); next_ch(); } sym = INT; } else if (ch >= 'a' && ch <= 'z') { int i = 0; /* missing overflow check */ while ((ch >= 'a' && ch <= 'z') || ch == '_'){ id_name[i++] = ch; next_ch(); } id_name[i] = '\0'; sym = 0; while (words[sym] != NULL && strcmp(words[sym], id_name) != 0) sym++; if (words[sym] == NULL) if (id_name[1] == '\0') sym = ID; else syntax_error(); } else syntax_error(); return; } Weak point: Path explosion
52. 25 Solver Directed Fuzzing • Collect path constraints • Solve negated constraints for new inputs
53. 25 Solver Directed Fuzzing • Collect path constraints • Solve negated constraints for new inputs
54. 26 Fuzzing Parsers $ ./fuzz [;x1-GPZ+wcckc];,N9J+?#6^6\e?]9lu
 2_%'4GX"0VUB[E/r ~fApu6b8<{%siq8Z
 h.6{V,hr?;{Ti.r3PIxMMMv6{xS^+'Hq!
 AxB"YXRS@!Kd6;wtAMefFWM(`|J_<1~o}
 z3K(CCzRH JIIvHz>_*.\>JrlU32~eGP?
 lR=bF3+;y$3lodQ<B89!5"W2fK*vE7v{'
 )KC-i,c{<[~m!]o;{.'}Gj\(X}EtYetrp
 bY@aGZ1{P!AZU7x#4(Rtn!q4nCwqol^y6
 }0|Ko=*JK~;zMKV=9Nai:wxu{J&UV#HaU
 )*BiC<),`+t*gka<W=Z.%T5WGHZpI30D<
 Pq>&]BS6R&j?#tP7iaV}-}`\?[_[Z^LBM
 PG-FKj'\xwuZ1=Q`^`5,$N$Q@[!CuRzJ2
 D|vBy!^zkhdf3C5PAkR?V((-%><hn|3='
 i2Qx]D$qs4O`1@fevnG'2\11Vf3piU37@
 5:dfd45*(7^%5ap\zIyl"'f,$ee,J4Gw:
 cgNKLie3nx9(`efSlg6#[K"@WjhZ}r[Sc
 un&sBCS,T[/3]KAeEnQ7lU)3Pn,0)G/6N
 -wyzj/MTd#A;r*(ds./df3r8Odaf?/<#r Interpreter
55. 26 Fuzzing Parsers $ ./fuzz [;x1-GPZ+wcckc];,N9J+?#6^6\e?]9lu
 2_%'4GX"0VUB[E/r ~fApu6b8<{%siq8Z
 h.6{V,hr?;{Ti.r3PIxMMMv6{xS^+'Hq!
 AxB"YXRS@!Kd6;wtAMefFWM(`|J_<1~o}
 z3K(CCzRH JIIvHz>_*.\>JrlU32~eGP?
 lR=bF3+;y$3lodQ<B89!5"W2fK*vE7v{'
 )KC-i,c{<[~m!]o;{.'}Gj\(X}EtYetrp
 bY@aGZ1{P!AZU7x#4(Rtn!q4nCwqol^y6
 }0|Ko=*JK~;zMKV=9Nai:wxu{J&UV#HaU
 )*BiC<),`+t*gka<W=Z.%T5WGHZpI30D<
 Pq>&]BS6R&j?#tP7iaV}-}`\?[_[Z^LBM
 PG-FKj'\xwuZ1=Q`^`5,$N$Q@[!CuRzJ2
 D|vBy!^zkhdf3C5PAkR?V((-%><hn|3='
 i2Qx]D$qs4O`1@fevnG'2\11Vf3piU37@
 5:dfd45*(7^%5ap\zIyl"'f,$ee,J4Gw:
 cgNKLie3nx9(`efSlg6#[K"@WjhZ}r[Sc
 un&sBCS,T[/3]KAeEnQ7lU)3Pn,0)G/6N
 -wyzj/MTd#A;r*(ds./df3r8Odaf?/<#r Parser Syntax Error Interpreter #
56. 27 Advanced Fuzzing: Specialized Generators • Specialize generation for a domain
57. 27 Advanced Fuzzing: Specialized Generators • Specialize generation for a domain
58. 27 Advanced Fuzzing: Specialized Generators • Specialize generation for a domain 80,000 lines of code
59. 28 The Holy Grail of Fuzzing
60. 28 The Holy Grail of Fuzzing Parsers
61. Overcoming Parsers
62. Overcoming Parsers
63. 30 Overcoming Parsers
64. 30 Overcoming Parsers
65. 30 Monolithic Overcoming Parsers
67. 32 The Missing Piece: Formal Specification
68. 33 Grammar
69. 34 Formal Languages Formal Language Descriptions
70. 34 Formal Languages Formal Language Descriptions 3. Regular (Chomsky,1956)
71. 34 Formal Languages Formal Language Descriptions 3. Regular Context Free (Chomsky,1956) Argument Stack
72. 34 Formal Languages Formal Language Descriptions 3. Regular Context Free Recursively Enumerable (Chomsky,1956) Argument Stack Return Stack
73. 34 Formal Languages Formal Language Descriptions 3. Regular Context Free Recursively Enumerable (Chomsky,1956) Easy to produce and parse Argument Stack Return Stack
74. 35 Grammar <start> := <expr> <expr> := <expr> '+' <expr> | <expr> '-' <expr> | <expr> '/' <expr> | <expr> '*' <expr> | '(' <expr> ')' | <number> <number> := <integer> | <integer> '.' <integer> <integer>:= <digit> <integer> | <digit> <digit> := [0-9] Arithmetic expression grammar
75. 35 Grammar <start> := <expr> <expr> := <expr> '+' <expr> | <expr> '-' <expr> | <expr> '/' <expr> | <expr> '*' <expr> | '(' <expr> ')' | <number> <number> := <integer> | <integer> '.' <integer> <integer>:= <digit> <integer> | <digit> <digit> := [0-9] Arithmetic expression grammar
76. 35 Grammar <start> := <expr> <expr> := <expr> '+' <expr> | <expr> '-' <expr> | <expr> '/' <expr> | <expr> '*' <expr> | '(' <expr> ')' | <number> <number> := <integer> | <integer> '.' <integer> <integer>:= <digit> <integer> | <digit> <digit> := [0-9] Arithmetic expression grammar <expr> key
77. 35 Grammar <start> := <expr> <expr> := <expr> '+' <expr> | <expr> '-' <expr> | <expr> '/' <expr> | <expr> '*' <expr> | '(' <expr> ')' | <number> <number> := <integer> | <integer> '.' <integer> <integer>:= <digit> <integer> | <digit> <digit> := [0-9] Arithmetic expression grammar Definition for <expr> <expr> key
78. 36 <start> := <expr> <expr> := <expr> '+' <expr> | <expr> '-' <expr> | <expr> '/' <expr> | <expr> '*' <expr> | '(' <expr> ')' | <number> <number> := <integer> | <integer> '.' <integer> <integer>:= <digit> <integer> | <digit> <digit> := [0-9] Grammar Arithmetic expression grammar
79. 36 <start> := <expr> <expr> := <expr> '+' <expr> | <expr> '-' <expr> | <expr> '/' <expr> | <expr> '*' <expr> | '(' <expr> ')' | <number> <number> := <integer> | <integer> '.' <integer> <integer>:= <digit> <integer> | <digit> <digit> := [0-9] Grammar Arithmetic expression grammar Expansion Rule
80. 36 <start> := <expr> <expr> := <expr> '+' <expr> | <expr> '-' <expr> | <expr> '/' <expr> | <expr> '*' <expr> | '(' <expr> ')' | <number> <number> := <integer> | <integer> '.' <integer> <integer>:= <digit> <integer> | <digit> <digit> := [0-9] Grammar Arithmetic expression grammar Expansion Rule Terminal Symbol
81. 36 <start> := <expr> <expr> := <expr> '+' <expr> | <expr> '-' <expr> | <expr> '/' <expr> | <expr> '*' <expr> | '(' <expr> ')' | <number> <number> := <integer> | <integer> '.' <integer> <integer>:= <digit> <integer> | <digit> <digit> := [0-9] Grammar Arithmetic expression grammar Expansion Rule Terminal Symbol Nonterminal Symbol
82. 36 <start> := <expr> <expr> := <expr> '+' <expr> | <expr> '-' <expr> | <expr> '/' <expr> | <expr> '*' <expr> | '(' <expr> ')' | <number> <number> := <integer> | <integer> '.' <integer> <integer>:= <digit> <integer> | <digit> <digit> := [0-9] Grammar Arithmetic expression grammar Expansion Rule Terminal Symbol Nonterminal Symbol
83. 37 Grammars As recognizers <start> := <expr> <expr> := <expr> '+' <expr> | <expr> '-' <expr> | <expr> '/' <expr> | <expr> '*' <expr> | '(' <expr> ')' | <number> <number> := <integer> | <integer> '.' <integer> <integer>:= <digit> <integer> | <digit> <digit> := [0-9]
84. 37 Grammars As recognizers (8 / 3) * 49 <start> := <expr> <expr> := <expr> '+' <expr> | <expr> '-' <expr> | <expr> '/' <expr> | <expr> '*' <expr> | '(' <expr> ')' | <number> <number> := <integer> | <integer> '.' <integer> <integer>:= <digit> <integer> | <digit> <digit> := [0-9]
85. 37 Grammars As recognizers (8 / 3) * 49 <start> := <expr> <expr> := <expr> '+' <expr> | <expr> '-' <expr> | <expr> '/' <expr> | <expr> '*' <expr> | '(' <expr> ')' | <number> <number> := <integer> | <integer> '.' <integer> <integer>:= <digit> <integer> | <digit> <digit> := [0-9]
86. 38 Grammars <start> := <expr> <expr> := <expr> '+' <expr> | <expr> '-' <expr> | <expr> '/' <expr> | <expr> '*' <expr> | '(' <expr> ')' | <number> <number> := <integer> | <integer> '.' <integer> <integer>:= <digit> <integer> | <digit> <digit> := [0-9] As producers (Hanford 1970) (Purdom 1972)
87. 38 Grammars8.2 - 27 - -9 / +((+9 * --2 + --+-+- ((-1 * +(8 - 5 - 6)) * (-(a-+(((+(4) )))) - ++4) / +(-+---((5.6 - --(3 * -1.8 * +(6 * +-(((-(-6) * ---+6)) / +--(+-+-7 * (-0 * (+(((((2)) + 8 - 3 - ++9.0 + ---(--+7 / (1 / +++6.37) + (1) / 482) / +++-+0)))) + 8.2 - 27 - -9 / +((+9 * --2 + --+-+-((-1 * + (8 - 5 - 6)) * (-(a-+(((+(4))))) - + +4) / +(-+---((5.6 - --(3 * -1.8 * + (6 * +-(((-(-6) * ---+6)) / +--(+-+- 7 * (-0 * (+(((((2)) + 8 - 3 - ++9.0 + ---(--+7 / (1 / +++6.37) + (1) / 482) / +++-+0)))) * -+5 + 7.513)))) - (+1 / ++((-84)))))))) * ++5 / +-(- -2 - -++-9.0)))) / 5 * --++090 + * - +5 + 7.513)))) - (+1 / ++((-84)))))) )) * 8.2 - 27 - -9 / +((+9 * --2 + - -+-+-((-1 * +(8 - 5 - 6)) * (-(a-+(( (+(4))))) - ++4) / +(-+---((5.6 - -- (3 * -1.8 * +(6 * +-(((-(-6) * ---+6 )) / +--(+-+-7 * (-0 * (+(((((2)) + 8 - 3 - ++9.0 + ---(--+7 / (1 / +++6 .37) + (1) / 482) / +++-+0)))) * -+5 + 7.513)))) - (+1 / ++((-84)))))))) * ++5 / +-(--2 - -++-9.0)))) / 5 * --++090 ++5 / +-(--2 - -++-9.0)))) / 5 * --++090 <start> := <expr> <expr> := <expr> '+' <expr> | <expr> '-' <expr> | <expr> '/' <expr> | <expr> '*' <expr> | '(' <expr> ')' | <number> <number> := <integer> | <integer> '.' <integer> <integer>:= <digit> <integer> | <digit> <digit> := [0-9] As producers (Hanford 1970) (Purdom 1972)
88. 39 Grammars As effective producers 8.2 - 27 - -9 / +((+9 * --2 + --+-+- ((-1 * +(8 - 5 - 6)) * (-(a-+(((+(4) )))) - ++4) / +(-+---((5.6 - --(3 * -1.8 * +(6 * +-(((-(-6) * ---+6)) / +--(+-+-7 * (-0 * (+(((((2)) + 8 - 3 - ++9.0 + ---(--+7 / (1 / +++6.37) + (1) / 482) / +++-+0)))) + 8.2 - 27 - -9 / +((+9 * --2 + --+-+-((-1 * + (8 - 5 - 6)) * (-(a-+(((+(4))))) - + +4) / +(-+---((5.6 - --(3 * -1.8 * + (6 * +-(((-(-6) * ---+6)) / +--(+-+- 7 * (-0 * (+(((((2)) + 8 - 3 - ++9.0 + ---(--+7 / (1 / +++6.37) + (1) / 482) / +++-+0)))) * -+5 + 7.513)))) - (+1 / ++((-84)))))))) * ++5 / +-(- -2 - -++-9.0)))) / 5 * --++090 + * - +5 + 7.513)))) - (+1 / ++((-84)))))) )) * 8.2 - 27 - -9 / +((+9 * --2 + - -+-+-((-1 * +(8 - 5 - 6)) * (-(a-+(( (+(4))))) - ++4) / +(-+---((5.6 - -- (3 * -1.8 * +(6 * +-(((-(-6) * ---+6 )) / +--(+-+-7 * (-0 * (+(((((2)) + 8 - 3 - ++9.0 + ---(--+7 / (1 / +++6 .37) + (1) / 482) / +++-+0)))) * -+5 + 7.513)))) - (+1 / ++((-84)))))))) * ++5 / +-(--2 - -++-9.0)))) / 5 * --++090 ++5 / +-(--2 - -++-9.0)))) / 5 * --++090
89. 39 Grammars As effective producers Interpreter Parser ✘ ✔ 8.2 - 27 - -9 / +((+9 * --2 + --+-+- ((-1 * +(8 - 5 - 6)) * (-(a-+(((+(4) )))) - ++4) / +(-+---((5.6 - --(3 * -1.8 * +(6 * +-(((-(-6) * ---+6)) / +--(+-+-7 * (-0 * (+(((((2)) + 8 - 3 - ++9.0 + ---(--+7 / (1 / +++6.37) + (1) / 482) / +++-+0)))) + 8.2 - 27 - -9 / +((+9 * --2 + --+-+-((-1 * + (8 - 5 - 6)) * (-(a-+(((+(4))))) - + +4) / +(-+---((5.6 - --(3 * -1.8 * + (6 * +-(((-(-6) * ---+6)) / +--(+-+- 7 * (-0 * (+(((((2)) + 8 - 3 - ++9.0 + ---(--+7 / (1 / +++6.37) + (1) / 482) / +++-+0)))) * -+5 + 7.513)))) - (+1 / ++((-84)))))))) * ++5 / +-(- -2 - -++-9.0)))) / 5 * --++090 + * - +5 + 7.513)))) - (+1 / ++((-84)))))) )) * 8.2 - 27 - -9 / +((+9 * --2 + - -+-+-((-1 * +(8 - 5 - 6)) * (-(a-+(( (+(4))))) - ++4) / +(-+---((5.6 - -- (3 * -1.8 * +(6 * +-(((-(-6) * ---+6 )) / +--(+-+-7 * (-0 * (+(((((2)) + 8 - 3 - ++9.0 + ---(--+7 / (1 / +++6 .37) + (1) / 482) / +++-+0)))) * -+5 + 7.513)))) - (+1 / ++((-84)))))))) * ++5 / +-(--2 - -++-9.0)))) / 5 * --++090 ++5 / +-(--2 - -++-9.0)))) / 5 * --++090
90. 40 Where to Get the Grammar From?
91. 41 •Reference Specification?
92. 41 The standard spec •Reference Specification?
93. 41 The standard spec Buggy Implementation •Reference Specification?
94. 41 The standard spec Buggy Implementation "Extra" Features •Reference Specification?
95. 41 The standard spec Buggy Implementation "Extra" Features "Be liberal in what you accept, and conservative in what you send"
 (the cause of trouble) Postel's Law "Accepted" Bugs •Reference Specification?
96. 42 https://www.json.org
97. 42 object { } { members } members pair pair , members pair string : value array [ ] [ elements ] elements value value , elements value string number object array true false null string " " " chars " chars char char chars char UNICODE \ [",\,CTRL] \" \\ \/ \b \f \n \r \t \u hex hex hex hex number int int frac int exp int frac exp int digit onenine digits - digit - onenine digits frac . digits exp e digits hex digit A - F a - f digits digit digit digits e e e+ e- E E+ E- https://www.json.org
98. 43 Parsing JSON is a Minefield http://seriot.ch/
99. 43 Parsing JSON is a Minefield http://seriot.ch/
100. 43 Parsing JSON is a Minefield http://seriot.ch/
101. 43 Parsing JSON is a Minefield http://seriot.ch/
102. 43 Parsing JSON is a Minefield http://seriot.ch/ Expected Parse Fail (Expect Success) Parse Success (Expect Fail) Parse Success (Undefined) Parse Fail (Undefined) Parser Crash Timeout
103. 43 Parsing JSON is a Minefield http://seriot.ch/ Expected Parse Fail (Expect Success) Parse Success (Expect Fail) Parse Success (Undefined) Parse Fail (Undefined) Parser Crash Timeout
105. 45 Where to Get the Grammar From?
106. 45 Where to Get the Grammar From? Hand-written parsers already encode the grammar
107. 46 How to Extract This Grammar?
108. 46 How to Extract This Grammar? • Inputs -> Dynamic Control Dependence Trees
109. 46 How to Extract This Grammar? • Inputs -> Dynamic Control Dependence Trees • DCD Trees -> Context Free Grammar
110. 47 Control Dependence Graph Statement B is control dependent on A if A determines whether B executes. def parse_csv(s,i): while s[i:]: if is_digit(s[i]): n,j = num(s[i:]) i = i+j else: comma(s[i]) i += 1
111. 47 Control Dependence Graph Statement B is control dependent on A if A determines whether B executes. def parse_csv(s,i): while s[i:]: if is_digit(s[i]): n,j = num(s[i:]) i = i+j else: comma(s[i]) i += 1 CDG for parse_csv
112. 47 Control Dependence Graph Statement B is control dependent on A if A determines whether B executes. def parse_csv(s,i): while s[i:]: if is_digit(s[i]): n,j = num(s[i:]) i = i+j else: comma(s[i]) i += 1 CDG for parse_csv while: determines whether if: executes
113. 48 def parse_csv(s,i): while s[i:]: if is_digit(s[i]): n,j = num(s[i:]) i = i+j else: comma(s[i]) i += 1 CDG for parse_csv Dynamic Control Dependence Tree Each statement execution is represented as a separate node
114. 48 def parse_csv(s,i): while s[i:]: if is_digit(s[i]): n,j = num(s[i:]) i = i+j else: comma(s[i]) i += 1 CDG for parse_csv Dynamic Control Dependence Tree Each statement execution is represented as a separate node DCD Tree for call parse_csv()
115. 49 def parse_csv(s,i): while s[i:]: if is_digit(s[i]): n,j = num(s[i:]) i = i+j else: comma(s[i]) i += 1 DCD Tree ~ Parse Tree •No tracking beyond input buffer •Characters are attached to nodes where they are accessed last "12," "12,"
116. 49 def parse_csv(s,i): while s[i:]: if is_digit(s[i]): n,j = num(s[i:]) i = i+j else: comma(s[i]) i += 1 '1' '2' ',' DCD Tree ~ Parse Tree •No tracking beyond input buffer •Characters are attached to nodes where they are accessed last "12," "12,"
117. 50 def is_digit(i): return i in '0123456789' def parse_num(s,i): n = '' while s[i:] and is_digit(s[i]): n += s[i] i = i +1 return i,n def parse_paren(s, i): assert s[i] == '(' i, v = parse_expr(s, i+1) if s[i:] == '': raise Ex(s, i) assert s[i] == ')' return i+1, v def parse_expr(s, i = 0): expr, is_op = [], True while s[i:]: c = s[i] if isdigit(c): if not is_op: raise Ex(s,i) i,num = parse_num(s,i) expr.append(num) is_op = False elif c in ['+', '-', '*', '/']: if is_op: raise Ex(s,i) expr.append(c) is_op, i = True, i + 1 elif c == '(': if not is_op: raise Ex(s,i) i, cexpr = parse_paren(s, i) expr.append(cexpr) is_op = False elif c == ')': break else: raise Ex(s,i) if is_op: raise Ex(s,i) return i, expr 9+3/4 Parse tree for parse_expr('9+3/4')
118. 50 def is_digit(i): return i in '0123456789' def parse_num(s,i): n = '' while s[i:] and is_digit(s[i]): n += s[i] i = i +1 return i,n def parse_paren(s, i): assert s[i] == '(' i, v = parse_expr(s, i+1) if s[i:] == '': raise Ex(s, i) assert s[i] == ')' return i+1, v def parse_expr(s, i = 0): expr, is_op = [], True while s[i:]: c = s[i] if isdigit(c): if not is_op: raise Ex(s,i) i,num = parse_num(s,i) expr.append(num) is_op = False elif c in ['+', '-', '*', '/']: if is_op: raise Ex(s,i) expr.append(c) is_op, i = True, i + 1 elif c == '(': if not is_op: raise Ex(s,i) i, cexpr = parse_paren(s, i) expr.append(cexpr) is_op = False elif c == ')': break else: raise Ex(s,i) if is_op: raise Ex(s,i) return i, expr 9+3/4 Parse tree for parse_expr('9+3/4')
119. 51 def is_digit(i): return i in '0123456789' def parse_num(s,i): n = '' while s[i:] and is_digit(s[i]): n += s[i] i = i +1 return i,n def parse_paren(s, i): assert s[i] == '(' i, v = parse_expr(s, i+1) if s[i:] == '': raise Ex(s, i) assert s[i] == ')' return i+1, v def parse_expr(s, i = 0): expr, is_op = [], True while s[i:]: c = s[i] if isdigit(c): if not is_op: raise Ex(s,i) i,num = parse_num(s,i) expr.append(num) is_op = False elif c in ['+', '-', '*', '/']: if is_op: raise Ex(s,i) expr.append(c) is_op, i = True, i + 1 elif c == '(': if not is_op: raise Ex(s,i) i, cexpr = parse_paren(s, i) expr.append(cexpr) is_op = False elif c == ')': break else: raise Ex(s,i) if is_op: raise Ex(s,i) return i, expr 9+3/4 Identifying Compatible Nodes Which nodes correspond to the same nonterminal
120. 51 def is_digit(i): return i in '0123456789' def parse_num(s,i): n = '' while s[i:] and is_digit(s[i]): n += s[i] i = i +1 return i,n def parse_paren(s, i): assert s[i] == '(' i, v = parse_expr(s, i+1) if s[i:] == '': raise Ex(s, i) assert s[i] == ')' return i+1, v def parse_expr(s, i = 0): expr, is_op = [], True while s[i:]: c = s[i] if isdigit(c): if not is_op: raise Ex(s,i) i,num = parse_num(s,i) expr.append(num) is_op = False elif c in ['+', '-', '*', '/']: if is_op: raise Ex(s,i) expr.append(c) is_op, i = True, i + 1 elif c == '(': if not is_op: raise Ex(s,i) i, cexpr = parse_paren(s, i) expr.append(cexpr) is_op = False elif c == ')': break else: raise Ex(s,i) if is_op: raise Ex(s,i) return i, expr 9+3/4 Identifying Compatible Nodes Which nodes correspond to the same nonterminal
121. 52 3 * (9 + 1)
122. 52 3 * (9 + 1)
123. 52 (9 + 1) * 3 3 * (9 + 1)
124. 52 (9 + 1) * 3 3 * (9 + 1)
125. 52 (9 + 1) * 3 3 * (9 + 1)
126. 53 3 * (9 + 1)
127. 53 3 * (9 + 1)
128. 53 9 + 1 3 * (9 + 1)
129. 53 9 + 1 3 * (9 + 1)
130. 53 9 + 1 3 * (9 + 1)
131. 54 3 * (9 + 1)
132. 54 3 (9 + 1) * 3 * (9 + 1)
133. 54 3 (9 + 1) * 3 * (9 + 1)
134. 54 3 (9 + 1) * 3 * (9 + 1)
135. 55 3*(1) 1
136. 56 3*(1) 1
137. 56 3*(1) 1 <parse_expr> := <while 1:1> <while 1:0> <while 1:1>
138. 56 3*(1) 1 <parse_expr> := <while 1:1> <while 1:0> <while 1:1> <while 1:1> <parse_expr> :=
139. <parse_expr> := <while 1:1> <while 1:0> <while 1:1> | <while 1:1> <while 1:0> <while 1:1> <while 1:0> <while 1:1> <while 1:0> <while 1:1> | <while 1:1> <while 1:0> <while 1:1> <while 1:0> <while 1:1> | <while 1:1> <while 1:1> := <if 1:1> <if 1:1> := <parse_num> | <parse_paren> <parse_num> := <is_digit> <is_digit> := '3' | '1' <parse_paren>:= '(' <parse_expr> ')' <while 1:0> := <if 1:0> <if 1:0> := '*' 57
140. <parse_expr> := <while_s> <while_s> := <while_1:1> <while_1:0> <while_s> | <while_1:1> <parse_expr> := <while 1:1> <while 1:0> <while 1:1> | <while 1:1> <while 1:0> <while 1:1> <while 1:0> <while 1:1> <while 1:0> <while 1:1> | <while 1:1> <while 1:0> <while 1:1> <while 1:0> <while 1:1> | <while 1:1> <while 1:1> := <if 1:1> <if 1:1> := <parse_num> | <parse_paren> <parse_num> := <is_digit> <is_digit> := '3' | '1' <parse_paren>:= '(' <parse_expr> ')' <while 1:0> := <if 1:0> <if 1:0> := '*' 57
141. 58 def is_digit(i): return i in '0123456789' def parse_num(s,i): n = '' while s[i:] and is_digit(s[i]): n += s[i] i = i +1 return i,n def parse_paren(s, i): assert s[i] == '(' i, v = parse_expr(s, i+1) if s[i:] == '': raise Ex(s, i) assert s[i] == ')' return i+1, v def parse_expr(s, i = 0): expr, is_op = [], True while s[i:]: c = s[i] if isdigit(c): if not is_op: raise Ex(s,i) i,num = parse_num(s,i) expr.append(num) is_op = False elif c in ['+', '-', '*', '/']: if is_op: raise Ex(s,i) expr.append(c) is_op, i = True, i + 1 elif c == '(': if not is_op: raise Ex(s,i) i, cexpr = parse_paren(s, i) expr.append(cexpr) is_op = False elif c == ')': break else: raise Ex(s,i) if is_op: raise Ex(s,i) return i, expr <START> := <parse_expr.0-0-c> <parse_expr.0-0-c> := <parse_expr.0-1-s><parse_expr.0> | <parse_expr.0> <parse_expr.0-1-s> := <parse_expr.0><parse_expr.0-2> | <parse_expr.0><parse_expr.0-2><parse_expr.0-1-s> <parse_expr.0> := '(' <parse_expr.0-0-c> ')' | <parse_num.0-1-s> <parse_expr.0-2> := '*' | '+' | '-' | '/' <parse_num.0-1-s> := <is_digit.0-0-c> | <is_digit.0-0-c><parse_num.0-1-s> <is_digit.0-0-c> : [0-9] calc.py Recovered Arithmetic Grammar
142. 59 <START> := <parse_expr.0-0-c> <parse_expr.0-0-c> := <parse_expr.0-1-s><parse_expr.0> | <parse_expr.0> <parse_expr.0-1-s> := <parse_expr.0><parse_expr.0-2> | <parse_expr.0><parse_expr.0-2><parse_expr.0-1-s> <parse_expr.0> := '(' <parse_expr.0-0-c> ')' | <parse_num.0-1-s> <parse_expr.0-2> := '*' | '+' | '-' | '/' <parse_num.0-1-s> := <is_digit.0-0-c> | <is_digit.0-0-c><parse_num.0-1-s> <is_digit.0-0-c> : [0-9]
143. 59 8.2 - 27 - -9 / +((+9 * --2 + --+-+- ((-1 * +(8 - 5 - 6)) * (-(a-+(((+(4) )))) - ++4) / +(-+---((5.6 - --(3 * -1.8 * +(6 * +-(((-(-6) * ---+6)) / +--(+-+-7 * (-0 * (+(((((2)) + 8 - 3 - ++9.0 + ---(--+7 / (1 / +++6.37) + (1) / 482) / +++-+0)))) + 8.2 - 27 - -9 / +((+9 * --2 + --+-+-((-1 * + (8 - 5 - 6)) * (-(a-+(((+(4))))) - + +4) / +(-+---((5.6 - --(3 * -1.8 * + (6 * +-(((-(-6) * ---+6)) / +--(+-+- 7 * (-0 * (+(((((2)) + 8 - 3 - ++9.0 + ---(--+7 / (1 / +++6.37) + (1) / 482) / +++-+0)))) * -+5 + 7.513)))) - (+1 / ++((-84)))))))) * ++5 / +-(- -2 - -++-9.0)))) / 5 * --++090 + * - +5 + 7.513)))) - (+1 / ++((-84)))))) )) * 8.2 - 27 - -9 / +((+9 * --2 + - -+-+-((-1 * +(8 - 5 - 6)) * (-(a-+(( (+(4))))) - ++4) / +(-+---((5.6 - -- (3 * -1.8 * +(6 * +-(((-(-6) * ---+6 )) / +--(+-+-7 * (-0 * (+(((((2)) + 8 - 3 - ++9.0 + ---(--+7 / (1 / +++6 .37) + (1) / 482) / +++-+0)))) * -+5 + 7.513)))) - (+1 / ++((-84)))))))) * ++5 / +-(--2 - -++-9.0)))) / 5 * --++090 ++5 / +-(--2 - -++-9.0)))) / 5 * --++090 <START> := <parse_expr.0-0-c> <parse_expr.0-0-c> := <parse_expr.0-1-s><parse_expr.0> | <parse_expr.0> <parse_expr.0-1-s> := <parse_expr.0><parse_expr.0-2> | <parse_expr.0><parse_expr.0-2><parse_expr.0-1-s> <parse_expr.0> := '(' <parse_expr.0-0-c> ')' | <parse_num.0-1-s> <parse_expr.0-2> := '*' | '+' | '-' | '/' <parse_num.0-1-s> := <is_digit.0-0-c> | <is_digit.0-0-c><parse_num.0-1-s> <is_digit.0-0-c> : [0-9]
144. 60 <START> ::= <json_raw> <json_raw> ::= '"' <json_string'> | '[' <json_list'> | '{' <json_dict'> | <json_number'> | 'true' | 'false' | 'null' <json_number'> ::= <json_number>+ | <json_number>+ 'e' <json_number>+ <json_number> ::= '+' | '-' | '.' | [0-9] | 'E' | 'e' <json_string'> ::= <json_string>* '"' <json_list'> ::= ']' | <json_raw> (','<json_raw>)* ']' | ( ',' <json_raw>)+ (',' <json_raw>)* ']' <json_dict'> ::= '}' | ( '"' <json_string'> ':' <json_raw> ',' )* '"'<json_string'> ':' <json_raw> '}' <json_string> ::= ' ' | '!' | '#' | '$' | '%' | '&' | ''' | '*' | '+' | '-' | ',' | '.' | '/' | ':' | ';' | '<' | '=' | '>' | '?' | '@' | '[' | ']' | '^' | '_', ''',| '{' | '|' | '}' | '~' | '[A-Za-z0-9]' | '\' <decode_escape> <decode_escape> ::= '"' | '/' | 'b' | 'f' | 'n' | 'r' | 't' stm.next() if expect_key: raise JSONError(E_DKEY, stm, stm.pos) if c == '}': return result expect_key = 1 continue # parse out a key/value pair elif c == '"': key = _from_json_string(stm) stm.skipspaces() c = stm.next() if c != ':': raise JSONError(E_COLON, stm, stm.pos) stm.skipspaces() val = _from_json_raw(stm) result[key] = val expect_key = 0 continue raise JSONError(E_MALF, stm, stm.pos) def _from_json_raw(stm): while True: stm.skipspaces() c = stm.peek() if c == '"': return _from_json_string(stm) elif c == '{': return _from_json_dict(stm) elif c == '[': return _from_json_list(stm) elif c == 't': return _from_json_fixed(stm, 'true', True, E_BOOL) elif c == 'f': return _from_json_fixed(stm, 'false', False, E_BOOL) elif c == 'n': return _from_json_fixed(stm, 'null', None, E_NULL) elif c in NUMSTART: return _from_json_number(stm) raise JSONError(E_MALF, stm, stm.pos) def from_json(data): stm = JSONStream(data) return _from_json_raw(stm) microjson.py Recovered JSON grammar
145. 61 <START> ::= <json_raw> <json_raw> ::= '"' <json_string'> | '[' <json_list'> | '{' <json_dict'> | <json_number'> | 'true' | 'false' | 'null' <json_number'> ::= <json_number>+ | <json_number>+ 'e' <json_number>+ <json_number> ::= '+' | '-' | '.' | [0-9] | 'E' | 'e' <json_string'> ::= <json_string>* '"' <json_list'> ::= ']' | <json_raw> (','<json_raw>)* ']' | ( ',' <json_raw>)+ (',' <json_raw>)* ']' <json_dict'> ::= '}' | ( '"' <json_string'> ':' <json_raw> ',' )* '"'<json_string'> ':' <json_raw> '}' <json_string> ::= ' ' | '!' | '#' | '$' | '%' | '&' | ''' | '*' | '+' | '-' | ',' | '.' | '/' | ':' | ';' | '<' | '=' | '>' | '?' | '@' | '[' | ']' | '^' | '_', ''',| '{' | '|' | '}' | '~' | '[A-Za-z0-9]' | '\' <decode_escape> <decode_escape> ::= '"' | '/' | 'b' | 'f' | 'n' | 'r' | 't' stm.next() if expect_key: raise JSONError(E_DKEY, stm, stm.pos) if c == '}': return result expect_key = 1 continue # parse out a key/value pair elif c == '"': key = _from_json_string(stm) stm.skipspaces() c = stm.next() if c != ':': raise JSONError(E_COLON, stm, stm.pos) stm.skipspaces() val = _from_json_raw(stm) result[key] = val expect_key = 0 continue raise JSONError(E_MALF, stm, stm.pos) def _from_json_raw(stm): while True: stm.skipspaces() c = stm.peek() if c == '"': return _from_json_string(stm) elif c == '{': return _from_json_dict(stm) elif c == '[': return _from_json_list(stm) elif c == 't': return _from_json_fixed(stm, 'true', True, E_BOOL) elif c == 'f': return _from_json_fixed(stm, 'false', False, E_BOOL) elif c == 'n': return _from_json_fixed(stm, 'null', None, E_NULL) elif c in NUMSTART: return _from_json_number(stm) raise JSONError(E_MALF, stm, stm.pos) def from_json(data): stm = JSONStream(data) return _from_json_raw(stm) microjson.py Recovered JSON grammar Mimid Gopinath, Mathis, and Zeller. Mining Input Grammars from Dynamic Control Flow. ESEC/FSE 2020. •Javascript •C •Lisp •JSON •URL •CGI
146. Actual Specification
147. Dynamic Approximation (Mimid) Actual Specification
148. Dynamic Approximation (Mimid) Static Approximation (Static Mimid) Actual Specification
149. Dynamic Approximation (Mimid) Static Approximation (Static Mimid) Actual Specification IOT & Embedded
151. Generating Unbiased Samples
152. Finding Good Samples Seed corpus?
153. Finding Good Samples Seed corpus? (Blind spots)
154. • Differentiate incomplete and incorrect inputs • Solve one input symbol at a time systematically Key Idea
155. 67 Sample Free Generators
156. 67 Sample Free Generators
157. 67 Sample Free Generators
158. 67 Sample Free Generators A
159. 67 Sample Free Generators A A ∉ (,+,-,1,2,3,4,5,6,7,8,9,0
160. 67 Sample Free Generators A ( A ∉ (,+,-,1,2,3,4,5,6,7,8,9,0
161. 67 Sample Free Generators A ( 2 A ∉ (,+,-,1,2,3,4,5,6,7,8,9,0
162. 67 Sample Free Generators A ( 2 - B 9 ) 4 ) A ∉ (,+,-,1,2,3,4,5,6,7,8,9,0 B ∉ +,-,1,2,3,4,5,6,7,8,9,0,) ) ∉ +,-,1,2,3,4,5,6,7,8,9,0
163. 67 Sample Free Generators A ( 2 - B 9 ) 4 ) A ∉ (,+,-,1,2,3,4,5,6,7,8,9,0 B ∉ +,-,1,2,3,4,5,6,7,8,9,0,) ) ∉ +,-,1,2,3,4,5,6,7,8,9,0
164. 67 Sample Free Generators A ( 2 - B 9 ) 4 ) A ∉ (,+,-,1,2,3,4,5,6,7,8,9,0 B ∉ +,-,1,2,3,4,5,6,7,8,9,0,) ) ∉ +,-,1,2,3,4,5,6,7,8,9,0 (2-94)
165. Mathis, Gopinath, Mera, Kampmann, Höschele, and Zeller. Parser Directed Fuzzing. PLDI 2019. Mathis, Gopinath and Zeller Learning Input Tokens for Effective Fuzzing. ISSTA 2020. Gopinath, Bendrissou, Mathis, and Zeller Black-box Testing with Monotonic Prefixes. ISSRE 2021 (submitted). Sample Free Generators A ( 2 - B 9 ) 4 )
166. <start> := <expr> <expr> := <expr> '+' <expr> | <expr> '-' <expr> | <expr> '/' <expr> | <expr> '*' <expr> | '(' <expr> ')' | <number> <number> := <integer> | <integer> '.' <integer> <integer>:= <digit> <integer> | <digit> <digit> := [0-9] Fast Fuzzing with Grammars fuzz(expr_grammar, '<start>')
167. <start> := <expr> <expr> := <expr> '+' <expr> | <expr> '-' <expr> | <expr> '/' <expr> | <expr> '*' <expr> | '(' <expr> ')' | <number> <number> := <integer> | <integer> '.' <integer> <integer>:= <digit> <integer> | <digit> <digit> := [0-9] Fast Fuzzing with Grammars fuzz(expr_grammar, '<start>') def fuzz(grammar, key): return collapse_tree(gen_key(grammar, key))
168. <start> := <expr> <expr> := <expr> '+' <expr> | <expr> '-' <expr> | <expr> '/' <expr> | <expr> '*' <expr> | '(' <expr> ')' | <number> <number> := <integer> | <integer> '.' <integer> <integer>:= <digit> <integer> | <digit> <digit> := [0-9] Fast Fuzzing with Grammars def gen_key(grammar, key):
 if is_terminal_symbol(key):
 return key else: next_rule = random.choice(rules) return gen_rule(grammar, grammar[key][next_rule]) fuzz(expr_grammar, '<start>') def fuzz(grammar, key): return collapse_tree(gen_key(grammar, key))
169. <start> := <expr> <expr> := <expr> '+' <expr> | <expr> '-' <expr> | <expr> '/' <expr> | <expr> '*' <expr> | '(' <expr> ')' | <number> <number> := <integer> | <integer> '.' <integer> <integer>:= <digit> <integer> | <digit> <digit> := [0-9] Fast Fuzzing with Grammars def gen_key(grammar, key):
 if is_terminal_symbol(key):
 return key else: next_rule = random.choice(rules) return gen_rule(grammar, grammar[key][next_rule]) fuzz(expr_grammar, '<start>') def fuzz(grammar, key): return collapse_tree(gen_key(grammar, key)) def gen_rule(grammar, rule): return [gen_key(token) for token in rule]
170. Fast Fuzzing with Grammars fuzz(expr_grammar, '<start>') def gen_key(grammar, key):
 if is_terminal_symbol(key):
 return key else: next_rule = random.choice(rules) return gen_rule(grammar, grammar[key][next_rule]) fuzz(expr_grammar, '<start>') def fuzz(grammar, key): return collapse_tree(gen_key(grammar, key)) def gen_rule(grammar, rule): return [gen_key(token) for token in rule]
171. Fast Fuzzing with Grammars <start> <expr> <expr> <expr> + <number> <number> <integer> <integer> <digit> <digit> 1 8 fuzz(expr_grammar, '<start>') def gen_key(grammar, key):
 if is_terminal_symbol(key):
 return key else: next_rule = random.choice(rules) return gen_rule(grammar, grammar[key][next_rule]) fuzz(expr_grammar, '<start>') def fuzz(grammar, key): return collapse_tree(gen_key(grammar, key)) def gen_rule(grammar, rule): return [gen_key(token) for token in rule]
172. Fast Fuzzing with Grammars <start> <expr> <expr> <expr> + <number> <number> <integer> <integer> <digit> <digit> 1 8 fuzz(expr_grammar, '<start>') def collapse(tree): key, children = tree if not children: return tree return ''.join([collapse(c) for c in children]) def gen_key(grammar, key):
 if is_terminal_symbol(key):
 return key else: next_rule = random.choice(rules) return gen_rule(grammar, grammar[key][next_rule]) fuzz(expr_grammar, '<start>') def fuzz(grammar, key): return collapse_tree(gen_key(grammar, key)) def gen_rule(grammar, rule): return [gen_key(token) for token in rule]
173. Fast Fuzzing with Grammars <start> <expr> <expr> <expr> + <number> <number> <integer> <integer> <digit> <digit> 1 8 fuzz(expr_grammar, '<start>') 1 8 + "1 + 8" def collapse(tree): key, children = tree if not children: return tree return ''.join([collapse(c) for c in children]) def gen_key(grammar, key):
 if is_terminal_symbol(key):
 return key else: next_rule = random.choice(rules) return gen_rule(grammar, grammar[key][next_rule]) fuzz(expr_grammar, '<start>') def fuzz(grammar, key): return collapse_tree(gen_key(grammar, key)) def gen_rule(grammar, rule): return [gen_key(token) for token in rule]
174. <start> := <expr> <expr> := <expr> '+' <expr> | <expr> '-' <expr> | <expr> '/' <expr> | <expr> '*' <expr> | '(' <expr> ')' | <number> <number> := <integer> | <integer> '.' <integer> <integer>:= <digit> <integer> | <digit> <digit> := [0-9] Compiling the Grammar
175. <start> := <expr> <expr> := <expr> '+' <expr> | <expr> '-' <expr> | <expr> '/' <expr> | <expr> '*' <expr> | '(' <expr> ')' | <number> <number> := <integer> | <integer> '.' <integer> <integer>:= <digit> <integer> | <digit> <digit> := [0-9] Compiling the Grammar def start(): expr() def expr(): match (random() % 6): case 0: expr(); print('+'); expr() case 1: expr(); print('-'); expr() case 2: expr(); print('/'); expr() case 3: expr(); print('*'); expr() case 4: print('('); expr(); print(')') case 5: number() def number(): match (random() % 2): case 0: integer() case 1: integer(); print('.'); integer() def integer(): match (random() % 2): case 0: digit(); integer() case 1: digit() def digit(): match (random() % 10): case 0: print('0') case 1: print('1') case 2: print('2') case 3: print('3') case 4: print('4') case 5: print('5') case 6: print('6') case 7: print('7')
176. <start> := <expr> <expr> := <expr> '+' <expr> | <expr> '-' <expr> | <expr> '/' <expr> | <expr> '*' <expr> | '(' <expr> ')' | <number> <number> := <integer> | <integer> '.' <integer> <integer>:= <digit> <integer> | <digit> <digit> := [0-9] Compiling the Grammar def start(): expr() def expr(): match (random() % 6): case 0: expr(); print('+'); expr() case 1: expr(); print('-'); expr() case 2: expr(); print('/'); expr() case 3: expr(); print('*'); expr() case 4: print('('); expr(); print(')') case 5: number() def number(): match (random() % 2): case 0: integer() case 1: integer(); print('.'); integer() def integer(): match (random() % 2): case 0: digit(); integer() case 1: digit() def digit(): match (random() % 10): case 0: print('0') case 1: print('1') case 2: print('2') case 3: print('3') case 4: print('4') case 5: print('5') case 6: print('6') case 7: print('7')
177. <start> := <expr> <expr> := <expr> '+' <expr> | <expr> '-' <expr> | <expr> '/' <expr> | <expr> '*' <expr> | '(' <expr> ')' | <number> <number> := <integer> | <integer> '.' <integer> <integer>:= <digit> <integer> | <digit> <digit> := [0-9] Compiling the Grammar def start(): expr() def expr(): match (random() % 6): case 0: expr(); print('+'); expr() case 1: expr(); print('-'); expr() case 2: expr(); print('/'); expr() case 3: expr(); print('*'); expr() case 4: print('('); expr(); print(')') case 5: number() def number(): match (random() % 2): case 0: integer() case 1: integer(); print('.'); integer() def integer(): match (random() % 2): case 0: digit(); integer() case 1: digit() def digit(): match (random() % 10): case 0: print('0') case 1: print('1') case 2: print('2') case 3: print('3') case 4: print('4') case 5: print('5') case 6: print('6') case 7: print('7') def start(rops): expr(rops) def expr(rops): match (rops.next % 6): case 0: expr(rops); print('+'); e case 1: expr(rops); print('-'); e case 2: expr(rops); print('/'); e case 3: expr(rops); print('*'); e case 4: print('('); expr(rops); p case 5: number(rops) def number(rops): match (rops.next % 2): case 0: integer(rops) case 1: integer(rops); print('.') def integer(rops): match (rops.next % 2): case 0: digit(rops); integer(rops case 1: digit(rops) def digit(rops): match (rops.next % 10): case 0: print('0') case 1: print('1') case 2: print('2') case 3: print('3') case 4: print('4') case 5: print('5') case 6: print('6') case 7: print('7')
178. <start> := <expr> <expr> := <expr> '+' <expr> | <expr> '-' <expr> | <expr> '/' <expr> | <expr> '*' <expr> | '(' <expr> ')' | <number> <number> := <integer> | <integer> '.' <integer> <integer>:= <digit> <integer> | <digit> <digit> := [0-9] Compiling the Grammar def start(): expr() def expr(): match (random() % 6): case 0: expr(); print('+'); expr() case 1: expr(); print('-'); expr() case 2: expr(); print('/'); expr() case 3: expr(); print('*'); expr() case 4: print('('); expr(); print(')') case 5: number() def number(): match (random() % 2): case 0: integer() case 1: integer(); print('.'); integer() def integer(): match (random() % 2): case 0: digit(); integer() case 1: digit() def digit(): match (random() % 10): case 0: print('0') case 1: print('1') case 2: print('2') case 3: print('3') case 4: print('4') case 5: print('5') case 6: print('6') case 7: print('7') def start(rops): expr(rops) def expr(rops): match (rops.next % 6): case 0: expr(rops); print('+'); e case 1: expr(rops); print('-'); e case 2: expr(rops); print('/'); e case 3: expr(rops); print('*'); e case 4: print('('); expr(rops); p case 5: number(rops) def number(rops): match (rops.next % 2): case 0: integer(rops) case 1: integer(rops); print('.') def integer(rops): match (rops.next % 2): case 0: digit(rops); integer(rops case 1: digit(rops) def digit(rops): match (rops.next % 10): case 0: print('0') case 1: print('1') case 2: print('2') case 3: print('3') case 4: print('4') case 5: print('5') case 6: print('6') case 7: print('7')
179. Grammar Fuzzer grammar = """
 <start> := <expr> <expr> := <expr> '+' <expr> | <expr> '-' <expr> | <expr> '/' <expr> | <expr> '*' <expr> | '(' <expr> ')' | <number> <number> := <integer> | <integer> '.' <integer> <integer>:= <digit> <integer> | <digit> <digit> := [0-9]
 """ generate(grammar) Fast Fuzzers def start(): expr() def expr(): match (random() % 6): case 0: expr(); print('+'); expr() case 1: expr(); print('-'); expr() case 2: expr(); print('/'); expr() case 3: expr(); print('*'); expr() case 4: print('('); expr(); print(')') case 5: number() def number(): match (random() % 2): case 0: integer() case 1: integer(); print('.'); integer() def integer(): match (random() % 2): case 0: digit(); integer() case 1: digit() def digit(): match (random() % 10): case 0: print('0') case 1: print('1') case 2: print('2') case 3: print('3') case 4: print('4') case 5: print('5') case 6: print('6') case 7: print('7') Compiled Grammar (F1) Building Fast Fuzzers Gopinath and Zeller 2019 def start_0(rops): r = next(rops) if 0 <= r < 43: expr_0() elif 43 <= r < 85: expr_1() elif 85 <= r < 128: expr_2() elif 128 <= r < 171: expr_3() elif 171 <= r < 213: expr_4() else: expr_5() def expr_0(rops): r = next(rops) if 0 <= r < 43: expr_0() elif 43 <= r < 85: expr_1() elif 85 <= r < 128: expr_2() elif 128 <= r < 171: expr_3() elif 171 <= r < 213: expr_4() else: expr_5() print('+') r = next(rops) if 0 <= r < 43: expr_0() elif 43 <= r < 85: expr_1() elif 85 <= r < 128: expr_2() elif 128 <= r < 171: expr_3() elif 171 <= r < 213: expr_4() else: expr_5() Grammar VM (F1)
180. 73 The Fuzzing Pipeline Program Under Test
181. 73 The Fuzzing Pipeline Program Under Test pFuzzer Active Guidance F1 Grammar Fuzzer Grammar Inputs Grammar Miner Samples Active Learning
182. 74 The Fuzzing Synergy Mimid Grammar Miner Parser Directed pFuzzer F1 Fuzzer VM Mathis, Gopinath, Mera, Kampmann, Höschele, and Zeller. Mining Input Grammars from Dynamic Control Flow. PLDI 2019. Mathis, Gopinath and Zeller Learning Input Tokens for Effective Fuzzing. ISSTA 2020. Gopinath, Bendrissou, Mathis, and Andreas Zeller Black-box Testing with Monotonic Prefixes. ISSTA 2021 (submitted). Gopinath and Zeller Building Fast Fuzzers 2019 (unpublished) Gopinath, Mathis, and Zeller Mining Input Grammars with Dynamic Control Flow. FSE 2020.
183. 74 The Fuzzing Synergy Mimid Grammar Miner Parser Directed pFuzzer F1 Fuzzer VM Mathis, Gopinath, Mera, Kampmann, Höschele, and Zeller. Mining Input Grammars from Dynamic Control Flow. PLDI 2019. Mathis, Gopinath and Zeller Learning Input Tokens for Effective Fuzzing. ISSTA 2020. Gopinath, Bendrissou, Mathis, and Andreas Zeller Black-box Testing with Monotonic Prefixes. ISSTA 2021 (submitted). Gopinath and Zeller Building Fast Fuzzers 2019 (unpublished) Gopinath, Mathis, and Zeller Mining Input Grammars with Dynamic Control Flow. FSE 2020.
184. 74 The Fuzzing Synergy Mimid Grammar Miner Parser Directed pFuzzer F1 Fuzzer VM Mathis, Gopinath, Mera, Kampmann, Höschele, and Zeller. Mining Input Grammars from Dynamic Control Flow. PLDI 2019. Mathis, Gopinath and Zeller Learning Input Tokens for Effective Fuzzing. ISSTA 2020. Gopinath, Bendrissou, Mathis, and Andreas Zeller Black-box Testing with Monotonic Prefixes. ISSTA 2021 (submitted). Gopinath and Zeller Building Fast Fuzzers 2019 (unpublished) Gopinath, Mathis, and Zeller Mining Input Grammars with Dynamic Control Flow. FSE 2020.
186. 76 Challenge: Multilevel Envelopes POST /InStock HTTP/1.1 Host: www.stock.org Content-Type: application/soap+xml; charset=utf-8 Content-Length: 312 <?xml version="1.0"?> <soap:Envelope xmlns:soap="http://www.w3.org/2001/12/soap-envelope" soap:encodingStyle="http://w3.org/2001/12/soap-encoding"> <soap:Body xmlns:m="http://www.stock.org/stock"> <m:GetStockPrice> <m:StockName>IBM</m:StockName> </m:GetStockPrice> </soap:Body> </soap:Envelope>
187. 76 Challenge: Multilevel Envelopes POST /InStock HTTP/1.1 Host: www.stock.org Content-Type: application/soap+xml; charset=utf-8 Content-Length: 312 <?xml version="1.0"?> <soap:Envelope xmlns:soap="http://www.w3.org/2001/12/soap-envelope" soap:encodingStyle="http://w3.org/2001/12/soap-encoding"> <soap:Body xmlns:m="http://www.stock.org/stock"> <m:GetStockPrice> <m:StockName>IBM</m:StockName> </m:GetStockPrice> </soap:Body> </soap:Envelope> HTTP POST
188. 76 Challenge: Multilevel Envelopes POST /InStock HTTP/1.1 Host: www.stock.org Content-Type: application/soap+xml; charset=utf-8 Content-Length: 312 <?xml version="1.0"?> <soap:Envelope xmlns:soap="http://www.w3.org/2001/12/soap-envelope" soap:encodingStyle="http://w3.org/2001/12/soap-encoding"> <soap:Body xmlns:m="http://www.stock.org/stock"> <m:GetStockPrice> <m:StockName>IBM</m:StockName> </m:GetStockPrice> </soap:Body> </soap:Envelope> HTTP POST XML PAYLOAD
189. 76 Challenge: Multilevel Envelopes POST /InStock HTTP/1.1 Host: www.stock.org Content-Type: application/soap+xml; charset=utf-8 Content-Length: 312 <?xml version="1.0"?> <soap:Envelope xmlns:soap="http://www.w3.org/2001/12/soap-envelope" soap:encodingStyle="http://w3.org/2001/12/soap-encoding"> <soap:Body xmlns:m="http://www.stock.org/stock"> <m:GetStockPrice> <m:StockName>IBM</m:StockName> </m:GetStockPrice> </soap:Body> </soap:Envelope> HTTP POST XML PAYLOAD SOAP
190. 76 Challenge: Multilevel Envelopes POST /InStock HTTP/1.1 Host: www.stock.org Content-Type: application/soap+xml; charset=utf-8 Content-Length: 312 <?xml version="1.0"?> <soap:Envelope xmlns:soap="http://www.w3.org/2001/12/soap-envelope" soap:encodingStyle="http://w3.org/2001/12/soap-encoding"> <soap:Body xmlns:m="http://www.stock.org/stock"> <m:GetStockPrice> <m:StockName>IBM</m:StockName> </m:GetStockPrice> </soap:Body> </soap:Envelope> HTTP POST XML PAYLOAD SOAP RPC Call
191. 77 Future Challenge: Multilevel Envelopes
192. 77 Future Challenge: Multilevel Envelopes
193. 77 Future Challenge: Multilevel Envelopes Mimid
194. 78 #include <stdio.h> int main() { int number1, number2, number3; number1 = 10; number2 = 20; number3 = sum(number1, number2); if (number3 > 100) return 0; return 1; } $ cc example.c -o example example.c 1.Syntactically correct 2.Variables declared before use 3.Use correct types 4.Statically conforming 5.Dynamically conforming 6.Model conforming Challenge: Semantic Envelopes (Mckeeman 1998) (parse) (compile) (link) (run) (synthesis)
195. 78 #include <stdio.h> int main() { int number1, number2, number3; number1 = 10; number2 = 20; number3 = sum(number1, number2); if (number3 > 100) return 0; return 1; } $ cc example.c -o example example.c 1.Syntactically correct 2.Variables declared before use 3.Use correct types 4.Statically conforming 5.Dynamically conforming 6.Model conforming Challenge: Semantic Envelopes (Mckeeman 1998) (parse) (compile) (link) (run) (synthesis)
196. 79 #include <stdio.h> int main() { int number1, number2, number3; number1 = 10; number2 = 20; number3 = sum(number1, number2); if (number3 > 100) return 0; return 1; } $ cc example.c -o example example.c 1.Syntactically correct 2.Variables declared before use 3.Use correct types 4.Statically conforming 5.Dynamically conforming 6.Model conforming Challenge: Semantic Envelopes (Mckeeman 1998) (parse) (compile) (link) (run) (synthesis)
198. 81 Fuzzing Inputs Program Behavior
199. 81 Fuzzing Inputs Program Behavior
200. 81 Fuzzing Inputs Program Behavior ✔
202. 83 We Found A Crash
203. 83 We Found A Crash
204. Why Did My Program Crash?
205. Why Did My Program Crash? 8.2 - 27 - -9 / +((+9 * --2 + --+-+-((-1 * +(8 - 5 - 6)) * (-(a-+(((+(4))))) - ++4) / +(-+---((5. 6 - --(3 * -1.8 * +(6 * +-(((-(-6) * ---+6)) / +- -(+-+-7 * (-0 * (+(((((2)) + 8 - 3 - ++9.0 + ---( --+7 / (1 / +++6.37) + (1) / 482) / +++-+0)))) + 8.2 - 27 - -9 / +((+9 * --2 + --+-+-((-1 * +(8 - 5 - 6)) * (-(a-+(((+(4))))) - ++4) / +(-+---((5.6 - --(3 * -1.8 * +(6 * +-(((-(-6) * ---+6)) / +-- (+-+-7 * (-0 * (+(((((2)) + 8 - 3 - ++9.0 + ---(- -+7 / (1 / +++6.37) + (1) / 482) / +++-+0)))) * - +5 + 7.513)))) - (+1 / ++((-84)))))))) * ++5 / +- (--2 - -++-9.0)))) / 5 * --++090 + * -+5 + 7.513) ))) - (+1 / ++((-84)))))))) * 8.2 - 27 - -9 / +(( +9 * --2 + --+-+-((-1 * +(8 - 5 - 6)) * (-(a-+ (((+(4))))) - ++4) / +(-+---((5.6 - --(3 * -1.8 * +(6 * +-(((-(-6) * ---+6)) / +--(+-+-7 * (-0 * ( +(((((2)) + 8 - 3 - ++9.0 + ---(--+7 / (1 / +++6. 37) + (1) / 482) / +++-+0)))) * -+5 + 7.513)))) - (+1 / ++((-84)))))))) * ++5 / +-(--2 - -++-9.0))) ) / 5 * --++090 ++5 / +-(--2 - -++-9.0)))) / 5 * --++090
206. Why Did My Program Crash? 8.2 - 27 - -9 / +((+9 * --2 + --+-+-((-1 * +(8 - 5 - 6)) * (-(a-+(((+(4))))) - ++4) / +(-+---((5. 6 - --(3 * -1.8 * +(6 * +-(((-(-6) * ---+6)) / +- -(+-+-7 * (-0 * (+(((((2)) + 8 - 3 - ++9.0 + ---( --+7 / (1 / +++6.37) + (1) / 482) / +++-+0)))) + 8.2 - 27 - -9 / +((+9 * --2 + --+-+-((-1 * +(8 - 5 - 6)) * (-(a-+(((+(4))))) - ++4) / +(-+---((5.6 - --(3 * -1.8 * +(6 * +-(((-(-6) * ---+6)) / +-- (+-+-7 * (-0 * (+(((((2)) + 8 - 3 - ++9.0 + ---(- -+7 / (1 / +++6.37) + (1) / 482) / +++-+0)))) * - +5 + 7.513)))) - (+1 / ++((-84)))))))) * ++5 / +- (--2 - -++-9.0)))) / 5 * --++090 + * -+5 + 7.513) ))) - (+1 / ++((-84)))))))) * 8.2 - 27 - -9 / +(( +9 * --2 + --+-+-((-1 * +(8 - 5 - 6)) * (-(a-+ (((+(4))))) - ++4) / +(-+---((5.6 - --(3 * -1.8 * +(6 * +-(((-(-6) * ---+6)) / +--(+-+-7 * (-0 * ( +(((((2)) + 8 - 3 - ++9.0 + ---(--+7 / (1 / +++6. 37) + (1) / 482) / +++-+0)))) * -+5 + 7.513)))) - (+1 / ++((-84)))))))) * ++5 / +-(--2 - -++-9.0))) ) / 5 * --++090 ++5 / +-(--2 - -++-9.0)))) / 5 * --++090 DD Minimized Input ((4))
207. Why Did My Program Crash? 8.2 - 27 - -9 / +((+9 * --2 + --+-+-((-1 * +(8 - 5 - 6)) * (-(a-+(((+(4))))) - ++4) / +(-+---((5. 6 - --(3 * -1.8 * +(6 * +-(((-(-6) * ---+6)) / +- -(+-+-7 * (-0 * (+(((((2)) + 8 - 3 - ++9.0 + ---( --+7 / (1 / +++6.37) + (1) / 482) / +++-+0)))) + 8.2 - 27 - -9 / +((+9 * --2 + --+-+-((-1 * +(8 - 5 - 6)) * (-(a-+(((+(4))))) - ++4) / +(-+---((5.6 - --(3 * -1.8 * +(6 * +-(((-(-6) * ---+6)) / +-- (+-+-7 * (-0 * (+(((((2)) + 8 - 3 - ++9.0 + ---(- -+7 / (1 / +++6.37) + (1) / 482) / +++-+0)))) * - +5 + 7.513)))) - (+1 / ++((-84)))))))) * ++5 / +- (--2 - -++-9.0)))) / 5 * --++090 + * -+5 + 7.513) ))) - (+1 / ++((-84)))))))) * 8.2 - 27 - -9 / +(( +9 * --2 + --+-+-((-1 * +(8 - 5 - 6)) * (-(a-+ (((+(4))))) - ++4) / +(-+---((5.6 - --(3 * -1.8 * +(6 * +-(((-(-6) * ---+6)) / +--(+-+-7 * (-0 * ( +(((((2)) + 8 - 3 - ++9.0 + ---(--+7 / (1 / +++6. 37) + (1) / 482) / +++-+0)))) * -+5 + 7.513)))) - (+1 / ++((-84)))))))) * ++5 / +-(--2 - -++-9.0))) ) / 5 * --++090 ++5 / +-(--2 - -++-9.0)))) / 5 * --++090 DD Minimized Input ((4)) 00000 ?
208. Why Did My Program Crash? 8.2 - 27 - -9 / +((+9 * --2 + --+-+-((-1 * +(8 - 5 - 6)) * (-(a-+(((+(4))))) - ++4) / +(-+---((5. 6 - --(3 * -1.8 * +(6 * +-(((-(-6) * ---+6)) / +- -(+-+-7 * (-0 * (+(((((2)) + 8 - 3 - ++9.0 + ---( --+7 / (1 / +++6.37) + (1) / 482) / +++-+0)))) + 8.2 - 27 - -9 / +((+9 * --2 + --+-+-((-1 * +(8 - 5 - 6)) * (-(a-+(((+(4))))) - ++4) / +(-+---((5.6 - --(3 * -1.8 * +(6 * +-(((-(-6) * ---+6)) / +-- (+-+-7 * (-0 * (+(((((2)) + 8 - 3 - ++9.0 + ---(- -+7 / (1 / +++6.37) + (1) / 482) / +++-+0)))) * - +5 + 7.513)))) - (+1 / ++((-84)))))))) * ++5 / +- (--2 - -++-9.0)))) / 5 * --++090 + * -+5 + 7.513) ))) - (+1 / ++((-84)))))))) * 8.2 - 27 - -9 / +(( +9 * --2 + --+-+-((-1 * +(8 - 5 - 6)) * (-(a-+ (((+(4))))) - ++4) / +(-+---((5.6 - --(3 * -1.8 * +(6 * +-(((-(-6) * ---+6)) / +--(+-+-7 * (-0 * ( +(((((2)) + 8 - 3 - ++9.0 + ---(--+7 / (1 / +++6. 37) + (1) / 482) / +++-+0)))) * -+5 + 7.513)))) - (+1 / ++((-84)))))))) * ++5 / +-(--2 - -++-9.0))) ) / 5 * --++090 ++5 / +-(--2 - -++-9.0)))) / 5 * --++090 DD Minimized Input ((4)) 00000 ? ((5)) ?
209. Why Did My Program Crash? 8.2 - 27 - -9 / +((+9 * --2 + --+-+-((-1 * +(8 - 5 - 6)) * (-(a-+(((+(4))))) - ++4) / +(-+---((5. 6 - --(3 * -1.8 * +(6 * +-(((-(-6) * ---+6)) / +- -(+-+-7 * (-0 * (+(((((2)) + 8 - 3 - ++9.0 + ---( --+7 / (1 / +++6.37) + (1) / 482) / +++-+0)))) + 8.2 - 27 - -9 / +((+9 * --2 + --+-+-((-1 * +(8 - 5 - 6)) * (-(a-+(((+(4))))) - ++4) / +(-+---((5.6 - --(3 * -1.8 * +(6 * +-(((-(-6) * ---+6)) / +-- (+-+-7 * (-0 * (+(((((2)) + 8 - 3 - ++9.0 + ---(- -+7 / (1 / +++6.37) + (1) / 482) / +++-+0)))) * - +5 + 7.513)))) - (+1 / ++((-84)))))))) * ++5 / +- (--2 - -++-9.0)))) / 5 * --++090 + * -+5 + 7.513) ))) - (+1 / ++((-84)))))))) * 8.2 - 27 - -9 / +(( +9 * --2 + --+-+-((-1 * +(8 - 5 - 6)) * (-(a-+ (((+(4))))) - ++4) / +(-+---((5.6 - --(3 * -1.8 * +(6 * +-(((-(-6) * ---+6)) / +--(+-+-7 * (-0 * ( +(((((2)) + 8 - 3 - ++9.0 + ---(--+7 / (1 / +++6. 37) + (1) / 482) / +++-+0)))) * -+5 + 7.513)))) - (+1 / ++((-84)))))))) * ++5 / +-(--2 - -++-9.0))) ) / 5 * --++090 ++5 / +-(--2 - -++-9.0)))) / 5 * --++090 DD Minimized Input ((4)) 00000 ? ((5)) ? (++5) ?
210. 85 Issue 386 from Rhino var A = class extends (class {}){}; Issue 2937 from Closure const [y,y] = []; var {baz:{} = baz => {}} = baz => {}; Issue 385 from Rhino {while ((l_0)){ if ((l_0)) {break;;var l_0; continue }0}} Issue 2842 from Closure
211. 85 Issue 386 from Rhino var A = class extends (class {}){}; Issue 2937 from Closure const [y,y] = []; var {baz:{} = baz => {}} = baz => {}; Issue 385 from Rhino {while ((l_0)){ if ((l_0)) {break;;var l_0; continue }0}} Issue 2842 from Closure
212. 85 Issue 386 from Rhino var A = class extends (class {}){}; Issue 2937 from Closure const [y,y] = []; var {baz:{} = baz => {}} = baz => {}; Issue 385 from Rhino {while ((l_0)){ if ((l_0)) {break;;var l_0; continue }0}} Issue 2842 from Closure
213. 85 Issue 386 from Rhino var A = class extends (class {}){}; Issue 2937 from Closure const [y,y] = []; var {baz:{} = baz => {}} = baz => {}; Issue 385 from Rhino {while ((l_0)){ if ((l_0)) {break;;var l_0; continue }0}} Issue 2842 from Closure
214. 85 Issue 386 from Rhino var A = class extends (class {}){}; Issue 2937 from Closure const [y,y] = []; var {baz:{} = baz => {}} = baz => {}; Issue 385 from Rhino {while ((l_0)){ if ((l_0)) {break;;var l_0; continue }0}} Issue 2842 from Closure Delta Minimization is useful but not sufficient
215. ( ( 4 ) )
216. ( ( 4 ) ) <start> := <expr> <expr> := <term> ' + ' <expr> | <term> ' - ' <expr> | <term> <term> := <factor> ' * ' <term> | <factor> ' / ' <term> | <factor> <factor> := '+' <factor> | '-' <factor> | '(' <expr> ')' | <integer> '.' <integer> | <integer> <integer>:= <digit> <integer> | <digit> <digit> := [0-9]
217. ( ( 4 ) )
218. ( ( 4 ) ) <start> := <expr> <expr> := <term> ' + ' <expr> | <term> ' - ' <expr> | <term> <term> := <factor> ' * ' <term> | <factor> ' / ' <term> | <factor> <factor> := '+' <factor> | '-' <factor> | '(' <expr> ')' | <integer> '.' <integer> | <integer> <integer>:= <digit> <integer> | <digit> <digit> := [0-9]
219. ( ( 4 ) ) <start> := <expr> <expr> := <term> ' + ' <expr> | <term> ' - ' <expr> | <term> <term> := <factor> ' * ' <term> | <factor> ' / ' <term> | <factor> <factor> := '+' <factor> | '-' <factor> | '(' <expr> ')' | <integer> '.' <integer> | <integer> <integer>:= <digit> <integer> | <digit> <digit> := [0-9]
220. ( ( 4 ) ) <start> := <expr> <expr> := <term> ' + ' <expr> | <term> ' - ' <expr> | <term> <term> := <factor> ' * ' <term> | <factor> ' / ' <term> | <factor> <factor> := '+' <factor> | '-' <factor> | '(' <expr> ')' | <integer> '.' <integer> | <integer> <integer>:= <digit> <integer> | <digit> <digit> := [0-9] ✓ Did not reproduce the failure 1 * (2 - 3)
221. ( ( 4 ) ) <start> := <expr> <expr> := <term> ' + ' <expr> | <term> ' - ' <expr> | <term> <term> := <factor> ' * ' <term> | <factor> ' / ' <term> | <factor> <factor> := '+' <factor> | '-' <factor> | '(' <expr> ')' | <integer> '.' <integer> | <integer> <integer>:= <digit> <integer> | <digit> <digit> := [0-9]
222. ( ( 4 ) ) <start> := <expr> <expr> := <term> ' + ' <expr> | <term> ' - ' <expr> | <term> <term> := <factor> ' * ' <term> | <factor> ' / ' <term> | <factor> <factor> := '+' <factor> | '-' <factor> | '(' <expr> ')' | <integer> '.' <integer> | <integer> <integer>:= <digit> <integer> | <digit> <digit> := [0-9] c
223. ( ( 4 ) ) <start> := <expr> <expr> := <term> ' + ' <expr> | <term> ' - ' <expr> | <term> <term> := <factor> ' * ' <term> | <factor> ' / ' <term> | <factor> <factor> := '+' <factor> | '-' <factor> | '(' <expr> ')' | <integer> '.' <integer> | <integer> <integer>:= <digit> <integer> | <digit> <digit> := [0-9] c
224. ( ( 4 ) ) <start> := <expr> <expr> := <term> ' + ' <expr> | <term> ' - ' <expr> | <term> <term> := <factor> ' * ' <term> | <factor> ' / ' <term> | <factor> <factor> := '+' <factor> | '-' <factor> | '(' <expr> ')' | <integer> '.' <integer> | <integer> <integer>:= <digit> <integer> | <digit> <digit> := [0-9] c ✓ Did not reproduce the failure 1 + 3 + 4
225. ( ( 4 ) ) <start> := <expr> <expr> := <term> ' + ' <expr> | <term> ' - ' <expr> | <term> <term> := <factor> ' * ' <term> | <factor> ' / ' <term> | <factor> <factor> := '+' <factor> | '-' <factor> | '(' <expr> ')' | <integer> '.' <integer> | <integer> <integer>:= <digit> <integer> | <digit> <digit> := [0-9] c c
226. 3 * 4 <start> := <expr> <expr> := <term> ' + ' <expr> | <term> ' - ' <expr> | <term> <term> := <factor> ' * ' <term> | <factor> ' / ' <term> | <factor> <factor> := '+' <factor> | '-' <factor> | '(' <expr> ')' | <integer> '.' <integer> | <integer> <integer>:= <digit> <integer> | <digit> <digit> := [0-9] c c
227. 3 * 4 <start> := <expr> <expr> := <term> ' + ' <expr> | <term> ' - ' <expr> | <term> <term> := <factor> ' * ' <term> | <factor> ' / ' <term> | <factor> <factor> := '+' <factor> | '-' <factor> | '(' <expr> ')' | <integer> '.' <integer> | <integer> <integer>:= <digit> <integer> | <digit> <digit> := [0-9] c c ✓ Did not reproduce the failure
228. ( ( 4 ) ) <start> := <expr> <expr> := <term> ' + ' <expr> | <term> ' - ' <expr> | <term> <term> := <factor> ' * ' <term> | <factor> ' / ' <term> | <factor> <factor> := '+' <factor> | '-' <factor> | '(' <expr> ')' | <integer> '.' <integer> | <integer> <integer>:= <digit> <integer> | <digit> <digit> := [0-9] c c c c c c c
229. ( ( 1 - 2 ) ) <start> := <expr> <expr> := <term> ' + ' <expr> | <term> ' - ' <expr> | <term> <term> := <factor> ' * ' <term> | <factor> ' / ' <term> | <factor> <factor> := '+' <factor> | '-' <factor> | '(' <expr> ')' | <integer> '.' <integer> | <integer> <integer>:= <digit> <integer> | <digit> <digit> := [0-9] c c c c c c c ( ( 1 - 2 ) )
230. ( ( 1 - 2 ) ) <start> := <expr> <expr> := <term> ' + ' <expr> | <term> ' - ' <expr> | <term> <term> := <factor> ' * ' <term> | <factor> ' / ' <term> | <factor> <factor> := '+' <factor> | '-' <factor> | '(' <expr> ')' | <integer> '.' <integer> | <integer> <integer>:= <digit> <integer> | <digit> <digit> := [0-9] c c c c c c c ✘ reproduced the failure ( ( 1 - 2 ) )
231. ( ( 1 - 2 ) ) c c c c c c c ( ( 1 - 2 ) )
232. ( ( 1 - 2 ) ) c c c c c c c ✘ ( ( 1 - 2 ) )
233. ( ( 1 - 2 ) ) c c c c c c c ✘ ( ( 1 - 2 ) ) ( ( 2 * 3 + 4 ) )
234. ( ( 1 - 2 ) ) c c c c c c c ✘ ( ( 1 - 2 ) ) ✘ ( ( 2 * 3 + 4 ) )
235. ( ( 1 - 2 ) ) c c c c c c c ✘ ( ( 1 - 2 ) ) ✘ ( ( 2 * 3 + 4 ) ) ( ( - 2 / 1 ) )
236. ( ( 1 - 2 ) ) c c c c c c c ✘ ( ( 1 - 2 ) ) ✘ ( ( 2 * 3 + 4 ) ) ✘ ( ( - 2 / 1 ) )
237. ( ( 1 - 2 ) ) c c c c c c c ✘ ( ( 1 - 2 ) ) ✘ ( ( 2 * 3 + 4 ) ) ✘ ( ( - 2 / 1 ) ) ( ( 98 - 0 ) )
238. ( ( 1 - 2 ) ) c c c c c c c ✘ ( ( 1 - 2 ) ) ✘ ( ( 2 * 3 + 4 ) ) ✘ ( ( - 2 / 1 ) ) ✘ ( ( 98 - 0 ) )
239. <expr> ) ( ( ) ( ( ) 4 ) ( ( 4 ) ) c c c c c c c A
240. <expr> ) ( ( ) ( ( ) 4 ) ( ( 4 ) ) c c c c c c c A
241. ( ( 4 ) ) c c c c c c c A ( ( ) ) <expr> ( ( ) ) 4 Minimized Input Abstract Failure Inducing Input def check(parsed): if parsed.is_nested() and parsed.child.is_nested(): raise Exception() return input
242. var A = class extends (class {}){}; Issue 2937 from Closure
243. var A = class extends (class {}){}; Issue 2937 from Closure <varModifier> <Identifier> = class extends (class {}){}
244. var {baz:{} = baz => {}} = baz => {}; Issue 385 from Rhino
245. var {baz:{} = baz => {}} = baz => {}; Issue 385 from Rhino var {<$Id1>:{} = <$Id1> => {}} <variableDeclaration>;
246. const [y,y] = []; Issue 386 from Rhino
247. const [y,y] = []; Issue 386 from Rhino const [<$Id1>,<$Id1>] = []
248. {while ((l_0)){ if ((l_0)) {break;;var l_0; continue }0}} Issue 2842 from Closure
249. {while ((l_0)){ if ((l_0)) {break;;var l_0; continue }0}} Issue 2842 from Closure {while ((<$Id1>)){ if ((<$Id1>)) {break;;var <$Id1>; continue }0}}
250. ( ( 4 ) ) c c c c c c c A ( ( ) ) <expr> ( ( ) ) 4 Minimized Input Abstract Failure Inducing Input • Effectively abstracts a minimized input • The abstraction identifies where the problem lies • Decompose complex program behaviors DDSET Gopinath, Kampmann, Havrikov, Soremekun, and Zeller. Abstracting Failure Inducing Inputs. ISSTA 2020. def check(parsed): if parsed.is_nested() and parsed.child.is_nested(): raise Exception() return input ISSTA 2020 Distinguished Award
251. 108 <start F> := <expr F> <expr F> := <term F> ' + ' <expr> | <term> ' + ' <expr F> | <term F> ' - ' <expr> | <term> ' - ' <expr F> | <term F> <term F> := <factor F> ' * ' <term> | <factor> ' * ' <term F> | <factor F> ' / ' <term> | <factor> ' / ' <term F> | <factor F> <factor F> := '+' <factor F> | '-' <factor F> | '(' <expr F> ')' | '(' <expr F1> ')' <expr F1> := <term F2> <term F2> := <factor F3> <factor F3>:= '(' <expr> ')' Specialized Grammar <factor F> is ((<expr>))
252. 108 <start F> := <expr F> <expr F> := <term F> ' + ' <expr> | <term> ' + ' <expr F> | <term F> ' - ' <expr> | <term> ' - ' <expr F> | <term F> <term F> := <factor F> ' * ' <term> | <factor> ' * ' <term F> | <factor F> ' / ' <term> | <factor> ' / ' <term F> | <factor F> <factor F> := '+' <factor F> | '-' <factor F> | '(' <expr F> ')' | '(' <expr F1> ')' <expr F1> := <term F2> <term F2> := <factor F3> <factor F3>:= '(' <expr> ')' ((1)) + 2 (23 * ((3)) - 34) (344- 4 + ((223))) (1) - 3 * 773 + (-22 + 1) 1798 - 889 / ((333-1)) * 2 / 3 + 1 34 + ((4)) -334 + (334 - (22) + 919 * 0 + 1 98435747+ 88 + (((0))) + (1) - 1 * 7 / 4 * 889 - 2 8 + ((8)) + --1 + 11223 / 344 - 39 + (1) - 456 + 134 / 45 437 + 8 - 1 * ((9 + ((1))) - 1 + 99111948 + 3 --1 + (112) - 2 + 445) + 0 74 + 334 + ((178 - 88 / (3393-1) * 1002 / 3 + 1+ 3439)) * 223 - 1233 + 334672 2 * ((9)) - (1798 - 889 / (333-1) * 2 / 3 + 100012 + 3434392 + 234 ----6 * 1798 - 889 / (33 778 - (((1) - 3 * 773 + (-22 + 1) * (4545) - 23 - ((2)) * 773 + (-22 + 1) / 3434 + ---1 + 1 / 34343 + 112 349 + (((1) - 3 * 3 + (-22 + 1) ((+ (-22 + 1) * (4545) - 23 - (2) * 773 + ((-22 + 1)) / 3434 + ---1 + 1 / 34343 + 1123 8 + ((8)) + --1 + / 1 - 39 + (1) - 456 + 134 / 45 ))(((1) - 2334 + ((((1)) - 3 * 773 + (-22 + 1) * (2) - 23 - (2) * 773 + (-22 + 1) / 3 74 + 3 + ((178 - 88 / (3393-1) * 1002 / 3 + 1+ 3439)) * - 1233 + 334672)) ((8 + ((8)) + --1 + / 344 - 39 + (1) - 456 + 134 / 45 ))(((1) - 3 * 773 1+ 33+ 24343433 +23343 - ((74 + 334 + ((178 - 88 / (3393-1) * 1002 / 3 + 1+ 3439)) * - 1233 + 334672)) ((8 + ((8)) + --1 + / 344 - 39 + (1) - 456 + 134 / 4 ✘ Specialized Grammar <factor F> is ((<expr>)) ✘
253. Algebra of Grammar Specializations
254. <variableDeclarationList C2937> is <varModifier> <Identifier> = class extends (class {}){} Closure 2937 <variableStatement R385> is var {<$Id2>:{} = <$Id2> => {}} <variableDeclaration>; Rhino 385 <variableDeclarationList R386> is const [<$Id3>,<$Id3>] = [] Rhino 386 <iterationStatement C2842> is {while ((<$Id1>)){ if ((<$Id1>)) {break;;var <$Id1>; continue }0}} Closure 2842 where Algebra of Grammar Specializations
255. <JavaScript C2937 and C2842> <variableDeclarationList C2937> is <varModifier> <Identifier> = class extends (class {}){} Closure 2937 <variableStatement R385> is var {<$Id2>:{} = <$Id2> => {}} <variableDeclaration>; Rhino 385 <variableDeclarationList R386> is const [<$Id3>,<$Id3>] = [] Rhino 386 <iterationStatement C2842> is {while ((<$Id1>)){ if ((<$Id1>)) {break;;var <$Id1>; continue }0}} Closure 2842 where Algebra of Grammar Specializations
256. <JavaScript C2937 and C2842> <JavaScript not(C2937 and C2842)> <variableDeclarationList C2937> is <varModifier> <Identifier> = class extends (class {}){} Closure 2937 <variableStatement R385> is var {<$Id2>:{} = <$Id2> => {}} <variableDeclaration>; Rhino 385 <variableDeclarationList R386> is const [<$Id3>,<$Id3>] = [] Rhino 386 <iterationStatement C2842> is {while ((<$Id1>)){ if ((<$Id1>)) {break;;var <$Id1>; continue }0}} Closure 2842 where Algebra of Grammar Specializations
257. <JavaScript C2937 and C2842> <JavaScript not(C2937 and C2842)> <JavaScript (C2937 or C2842) and (R385 or R386)> <variableDeclarationList C2937> is <varModifier> <Identifier> = class extends (class {}){} Closure 2937 <variableStatement R385> is var {<$Id2>:{} = <$Id2> => {}} <variableDeclaration>; Rhino 385 <variableDeclarationList R386> is const [<$Id3>,<$Id3>] = [] Rhino 386 <iterationStatement C2842> is {while ((<$Id1>)){ if ((<$Id1>)) {break;;var <$Id1>; continue }0}} Closure 2842 where Algebra of Grammar Specializations
258. Gopinath, Nemati, Zeller. Input Algebras. ICSE 2021. Mechanized proofs are available Algebra of Grammar Specializations
259. Gopinath, Nemati, Zeller. Input Algebras. ICSE 2021. <JavaScript not(C2937 or C2842 or R385 or R386)> where <variableDeclarationList C2937> is <varModifier> <Identifier> = class extends (class {}){} <iterationStatement C2842> is {while ((<$Id1>)){ if ((<$Id1>)) {break;;var <$Id1>; continue }0}} <variableStatement R385> is var {<$Id2>:{} = <$Id2> => {}} <variableDeclaration>; <variableDeclarationList R386> is const [<$Id3>,<$Id3>] = [] Mechanized proofs are available Algebra of Grammar Specializations
265. Science of Focused Fuzzing <expr E & F> where <factor E> is ((<expr>)) <factor F> is <term> / 0
266. <expr E & F> where <factor E> is ((<expr>)) <factor F> is <term> / 0
267. <expr E & F> where <factor E> is ((<expr>)) <factor F> is <term> / 0 Isolating & Decomposing Program Behaviors
268. <expr E & F> where <factor E> is ((<expr>)) <factor F> is <term> / 0 Isolating & Decomposing Program Behaviors Algebra of Program Behaviors
269. <expr E & F> where <factor E> is ((<expr>)) <factor F> is <term> / 0 Isolating & Decomposing Program Behaviors Algebra of Program Behaviors Science of Program Behaviors
271. 115 insert into tbl values (1,2,3) select b from tbl drop table tbl Input Behavior Program Challenge: Identify Behavior Divergence
272. 115 insert into tbl values (1,2,3) select b from tbl drop table tbl update($file) read($file) rm($file) Input Behavior action='read' $action('tbl') Program assert invoked read: 'tbl.data' ✔ Challenge: Identify Behavior Divergence
273. 115 insert into tbl values (1,2,3) select b from tbl drop table tbl update($file) read($file) rm($file) Input Behavior action='read' $action('tbl') Program assert invoked read: 'tbl.data' ✔ action='rm' Challenge: Identify Behavior Divergence
274. 115 insert into tbl values (1,2,3) select b from tbl drop table tbl update($file) read($file) rm($file) Input Behavior action='read' $action('tbl') Program assert invoked read: 'tbl.data' ✔ action='rm' Challenge: Identify Behavior Divergence
275. def triangle(a, b, c): if a == b: if b == c: return Equilateral else: return Isosceles else: if b == c: return Isosceles else: if a == c: return Isosceles else: return Scalene Challenge: Identify Behavior Divergence
276. def triangle(a, b, c): if a == b: if b == c: return Equilateral else: return Isosceles else: if b == c: return Isosceles else: if a == c: return Isosceles else: return Scalene Challenge: Identify Behavior Divergence
277. Challenge: Identify Behavior Divergence LockB() LockA() DoAB() UnlockB() UnlockA()
278. Challenge: Identify Behavior Divergence LockB() LockA() DoAB() UnlockB() UnlockA()
279. Challenge: Identify Behavior Divergence LockB() LockA() DoAB() UnlockB() UnlockA() LockB() LockA() DoAB() UnlockA() UnlockB()
280. Challenge: Identify Behavior Divergence LockB() LockA() DoAB() UnlockB() UnlockA() LockB() LockA() DoAB() UnlockA() UnlockB() UnLockA() LockA() DoAB() LockB() UnlockB()
281. 118 def triangle(a, b, c): if a == b: if b == c: return Equilateral else: return Isosceles else: if b == c: return Isosceles else: if a == c: return Isosceles else: return Scalene
282. 118 def triangle(a, b, c): if a == b: if b == c: return Equilateral else: return Isosceles else: if b == c: return Isosceles else: if a == c: return Isosceles else: return Scalene
284. 119 <enter> := <triangle(a,b,c)>
285. 120 <enter> := <triangle(a,b,c)> <triangle(a,b,c)> := (a==b) <if_2 T> | (a!=b) <if_2 F>
286. 121 <enter> := <triangle(a,b,c)> <triangle(a,b,c)> := (a==b) <if_2 T> | (a!=b) <if_2 F> <if_2 T> := (b==c) <if_3 T> | (b!=c) <if_3 F>
287. 122 <enter> := <triangle(a,b,c)> <triangle(a,b,c)> := (a==b) <if_2 T> | (a!=b) <if_2 F> <if_2 T> := (b==c) <if_3 T> | (b!=c) <if_3 F> <if_3 T> := "return Equilateral" <if_3 F> := "return Isosceles"
288. 123 <enter> := <triangle(a,b,c)> <triangle(a,b,c)> := (a==b) <if_2 T> | (a!=b) <if_2 F> <if_2 T> := (b==c) <if_3 T> | (b!=c) <if_3 F> <if_3 T> := "return Equilateral" <if_3 F> := "return Isosceles" <if_2 F> := (b==c) <if_8 T> | (b!=c) <if_8 F> <if_8 T> := "return Isosceles" <if_8 F> := (a==c) <if_11 T> | (a!=c) <if_11 F> <if_11 T> := "return Isosceles" <if_11 F> := "return Scalene"
289. LockB() LockA() DoAB() UnlockB() UnlockA() Challenge: Identify Behavior Divergence "lockA" "lockB" <DoAB> "UnlockB" "UnlockA"
291. 126 The Science of Inputs Program The Science of Behaviors ✔
292. 126 The Science of Inputs Program The Science of Behaviors ✔
293. 126 The Science of Inputs Program The Science of Behaviors ✔
294. 126 The Science of Fuzzing The Science of Inputs Program The Science of Behaviors ✔
296. 128 Oracles for Fuzzing Focused Fuzzing Automatic Repair Fault Localization Beyond Syntax Grammar Mining
297. 128 Oracles for Fuzzing Focused Fuzzing Automatic Repair Fault Localization Beyond Syntax Grammar Mining Onward
298. Program Under Test pFuzzer F1 Fuzzer Inputs Grammar Miner https://rahul.gopinath.org
299. Program Under Test pFuzzer F1 Fuzzer Inputs Grammar Miner https://rahul.gopinath.org
300. Program Under Test pFuzzer F1 Fuzzer Inputs Grammar Miner https://rahul.gopinath.org
301. Program Under Test pFuzzer F1 Fuzzer Inputs Grammar Miner https://rahul.gopinath.org
302. Program Under Test pFuzzer F1 Fuzzer Inputs Grammar Miner Problem: How to Fuzz Parsers https://rahul.gopinath.org
303. Program Under Test pFuzzer F1 Fuzzer Inputs Grammar Miner Problem: How to Fuzz Parsers https://rahul.gopinath.org Generalize
304. Program Under Test pFuzzer F1 Fuzzer Inputs Grammar Miner Problem: How to Fuzz Parsers https://rahul.gopinath.org Generalize Combine
305. Future Work: Program Under Test pFuzzer F1 Fuzzer Inputs Grammar Miner Problem: How to Fuzz Parsers https://rahul.gopinath.org Generalize Combine The Science of Fuzzing
306. Future Work: Program Under Test pFuzzer F1 Fuzzer Inputs Grammar Miner Problem: How to Fuzz Parsers https://rahul.gopinath.org Debugging Combine The Science of Fuzzing