Deciding The Precongruence For Deadlock Freedom Using Operating Guidelines

In the context of asynchronously communicating and deadlock free services, the refinement relation of services has been formalized by the accordance preorder. A service Impl accords with a service Spec if every controller of Spec—that is, every environment that can interact with service Spec without deadlocking—is a controller of Impl. The procedure to decide accordance of two services uses that the set of controllers of a finite-state service has a finite representation, called operating guideline. Recently, it has been shown that the accordance preorder is not a precongruence and thus the decision procedure based on operating guidelines cannot be used. In this paper, we adapt the results on operating guidelines to the precongruence setting: We define an operating guideline that represents all controllers of a service w.r.t. the accordance precongruence and show how this refinement relation of two services can be decided based on their operating guidelines.

I gave this talk at the 2nd workshop on Petri nets compositions (CompoNet) 2012, Satellite of PETRI NETS 2012, June 25-29 2012, Hamburg, Germany.

Transcript

1. RICHARD MÜLLER CHRISTIAN STAHL L R DECIDING THE PRECONGRUENCE FOR DEADLOCK FREEDOM USING OPERATING GUIDELINES
2. SERVICE SETTING 2 SERVICE SERVICE A L
3. SERVICE SETTING 2 A L SERVICE SERVICE A⊕L COMPOSITION
4. SERVICE SETTING 2 A L SERVICE SERVICE A⊕L COMPOSITION DEF: CONTROLLER A CONTROLS L IFF A⊕L IS DEADLOCK FREE AND BOUNDED
5. SERVICE SUBSTITUTION 3 A L R
6. SERVICE SUBSTITUTION 3 L R ⊆
7. SERVICE SUBSTITUTION 3 L R ⊆ DEF: ACCORDANCE R ACCORDS WITH L IFF FOR ALL A: A CONTROLS L IMPLIES A CONTROLS R
8. ACCORDANCE 4 GENERAL CASE SPECIAL CASE UNIVERSE ALL SERVICES INNERLY BOUNDED SERVICES PRESERVED UNDER COMPOSITION? YES NO DECIDABLE? WITH TRACE-BASED SEMANTICS WITH OPERATING GUIDELINES
9. ACCORDANCE 4 GENERAL CASE SPECIAL CASE UNIVERSE ALL SERVICES INNERLY BOUNDED SERVICES PRESERVED UNDER COMPOSITION? YES NO DECIDABLE? WITH TRACE-BASED SEMANTICS WITH OPERATING GUIDELINES
10. ACCORDANCE 4 GENERAL CASE SPECIAL CASE UNIVERSE ALL SERVICES INNERLY BOUNDED SERVICES PRESERVED UNDER COMPOSITION? YES NO DECIDABLE? WITH TRACE-BASED SEMANTICS WITH OPERATING GUIDELINES
11. ACCORDANCE 4 GENERAL CASE SPECIAL CASE UNIVERSE ALL SERVICES INNERLY BOUNDED SERVICES PRESERVED UNDER COMPOSITION? YES NO DECIDABLE? WITH TRACE-BASED SEMANTICS WITH OPERATING GUIDELINES B
12. ACCORDANCE 4 GENERAL CASE SPECIAL CASE UNIVERSE ALL SERVICES INNERLY BOUNDED SERVICES PRESERVED UNDER COMPOSITION? YES NO DECIDABLE? WITH TRACE-BASED SEMANTICS WITH OPERATING GUIDELINES DECIDE WITH OPERATING GUIDELINES? B
13. OUTLINE UNIVERSE ALL SERVICES INNERLY BOUNDED SERVICES PRESERVED UNDER COMPOSITION? YES NO DECIDABLE? WITH TRACE-BASED SEMANTICS WITH OPERATING GUIDELINES DECIDE WITH OPERATING GUIDELINES? 1. DIFFERENCE B
14. OUTLINE UNIVERSE ALL SERVICES INNERLY BOUNDED SERVICES PRESERVED UNDER COMPOSITION? YES NO DECIDABLE? WITH TRACE-BASED SEMANTICS WITH OPERATING GUIDELINES DECIDE WITH OPERATING GUIDELINES? 1. DIFFERENCE 2. B
15. OUTLINE UNIVERSE ALL SERVICES INNERLY BOUNDED SERVICES PRESERVED UNDER COMPOSITION? YES NO DECIDABLE? WITH TRACE-BASED SEMANTICS WITH OPERATING GUIDELINES DECIDE WITH OPERATING GUIDELINES? 1. DIFFERENCE 2. 3. B
16. OUTLINE UNIVERSE ALL SERVICES INNERLY BOUNDED SERVICES PRESERVED UNDER COMPOSITION? YES NO DECIDABLE? WITH TRACE-BASED SEMANTICS WITH OPERATING GUIDELINES DECIDE WITH OPERATING GUIDELINES? 1. DIFFERENCE B
17. THE DIFFERENCE 6 UNIVERSE ALL SERVICES INNERLY BOUNDED SERVICES PRESERVED UNDER COMPOSITION? YES NO DECIDABLE? WITH TRACE-BASED SEMANTICS WITH OPERATING GUIDELINES DECIDE WITH OPERATING GUIDELINES? C B
18. THE DIFFERENCE 6 UNIVERSE ALL SERVICES INNERLY BOUNDED SERVICES PRESERVED UNDER COMPOSITION? YES NO DECIDABLE? WITH TRACE-BASED SEMANTICS WITH OPERATING GUIDELINES DECIDE WITH OPERATING GUIDELINES? C B U UB
19. THE DIFFERENCE 6 UNIVERSE ALL SERVICES INNERLY BOUNDED SERVICES PRESERVED UNDER COMPOSITION? YES NO DECIDABLE? WITH TRACE-BASED SEMANTICS WITH OPERATING GUIDELINES DECIDE WITH OPERATING GUIDELINES? C B CONT⊆UxU U UB ACC ⊆UxU
20. THE DIFFERENCE 6 UNIVERSE ALL SERVICES INNERLY BOUNDED SERVICES PRESERVED UNDER COMPOSITION? YES NO DECIDABLE? WITH TRACE-BASED SEMANTICS WITH OPERATING GUIDELINES DECIDE WITH OPERATING GUIDELINES? C B CONT⊆UxU U UB CONT⊆UBxUB ACC ⊆UxU ACC ⊆UBxUB
21. THE DIFFERENCE 6 UNIVERSE ALL SERVICES INNERLY BOUNDED SERVICES PRESERVED UNDER COMPOSITION? YES NO DECIDABLE? WITH TRACE-BASED SEMANTICS WITH OPERATING GUIDELINES DECIDE WITH OPERATING GUIDELINES? C B CONT⊆UxU U UB CONT⊆UBxUB ACC ⊆UxU ACC ⊆UBxUB SPECIAL CASE: RESTRICTS CONTROLLER AND ACCORDANCE
22. SERVICE MODEL: OPEN NETS 7 A L
23. SERVICE MODEL: OPEN NETS 7 A⊕L
24. 8 A L INFLUENCES OF THE UNIVERSE R
25. 8 A L GENERAL CASE: A CONTROLS L AND R INFLUENCES OF THE UNIVERSE R SPECIAL CASE: A CONTROLS L AND R
26. 9 B INFLUENCES OF THE UNIVERSE INNERLY UNBOUNDED
27. 9 B INFLUENCES OF THE UNIVERSE INNERLY UNBOUNDED
28. 9 B INFLUENCES OF THE UNIVERSE L R
29. 9 B INFLUENCES OF THE UNIVERSE L R SPECIAL CASE: B NOT CONSIDERED
30. 9 B GENERAL CASE: B CONTROLS L B DOES NOT CONTROL R INFLUENCES OF THE UNIVERSE L R SPECIAL CASE: B NOT CONSIDERED
31. 9 B GENERAL CASE: B CONTROLS L B DOES NOT CONTROL R INFLUENCES OF THE UNIVERSE GENERAL CASE: R DOES NOT ACCORD WITH L L R SPECIAL CASE: B NOT CONSIDERED
32. OUTLINE UNIVERSE ALL SERVICES INNERLY BOUNDED SERVICES PRESERVED UNDER COMPOSITION? YES NO DECIDABLE? WITH TRACE-BASED SEMANTICS WITH OPERATING GUIDELINES DECIDE WITH OPERATING GUIDELINES? 1. DIFFERENCE B
33. OUTLINE UNIVERSE ALL SERVICES INNERLY BOUNDED SERVICES PRESERVED UNDER COMPOSITION? YES NO DECIDABLE? WITH TRACE-BASED SEMANTICS WITH OPERATING GUIDELINES DECIDE WITH OPERATING GUIDELINES? 2. B
34. OPERATING GUIDELINE 11 L R ⊆
35. OPERATING GUIDELINE 11 L R ⊆ OG(L) OG(R)
36. OPERATING GUIDELINE 11 L R ⊆ OG(L) OG(R) ~REF
37. OPERATING GUIDELINE 11 L R ⊆ OG(L) OG(R) ~REF
38. OPERATING GUIDELINE 11 L R ⊆ OG(L) OG(R) ~REF B
39. OPERATING GUIDELINE 12 R OG(R) ?a ?a τ τ τ ?a a VIEWPOINT OF CONTROLLER
40. OPERATING GUIDELINE 12 R OG(R) ?a ?a τ τ τ ?a a ∅ EMPTY NODE ENCODES UNREACHABLE BEHAVIOR
41. OPERATING GUIDELINE 12 R OG(R) ?a ?a τ τ τ ?a a A a ?a BEH(A) τ ∅ EMPTY NODE ENCODES UNREACHABLE BEHAVIOR
42. OPERATING GUIDELINE 13 R OG(R) ?a ?a τ τ τ ?a a D a ?a BEH(D) τ τ ∅ EMPTY NODE ENCODES UNREACHABLE BEHAVIOR
43. OPERATING GUIDELINE 13 R OG(R) ?a ?a τ τ τ ?a a D a ?a BEH(D) τ τ ∅ FORMULA(NODE) ENCODES VALID BEHAVIORS TRUE TRUE TRUE
44. OPERATING GUIDELINE 14 L OG(L) R OG(R) ∅ ?a ?a τ τ τ ?a ∅ ?a τ τ ?a a a FORMULA(NODE) ENCODES VALID BEHAVIORS TRUE TRUE TRUE
45. OPERATING GUIDELINE 14 L OG(L) R OG(R) ∅ ?a ?a τ τ τ ?a ∅ ?a τ τ ?a a a FORMULA(NODE) ENCODES VALID BEHAVIORS TRUE TRUE TRUE TRUE TRUE
46. DECIDE SPECIAL CASE: ~REF 15 L OG(L) R OG(R) ∅ ?a ?a τ τ τ ?a ∅ ?a τ τ ?a a a 1) OG(L) SIMULATED BY OG(R) 2) FOR (l,r): FORMULA(l) IMPLIES FORMULA (r)
47. DECIDE SPECIAL CASE: ~REF 15 L OG(L) R OG(R) ∅ ?a ?a τ τ τ ?a ∅ ?a τ τ ?a a a 1) OG(L) SIMULATED BY OG(R) 2) FOR (l,r): FORMULA(l) IMPLIES FORMULA (r)
48. DECIDE SPECIAL CASE: ~REF 15 L OG(L) R OG(R) ∅ ?a ?a τ τ τ ?a ∅ ?a τ τ ?a a a 1) OG(L) SIMULATED BY OG(R) 2) FOR (l,r): FORMULA(l) IMPLIES FORMULA (r)
49. DECIDE SPECIAL CASE: ~REF 15 L OG(L) R OG(R) ∅ ?a ?a τ τ τ ?a ∅ ?a τ τ ?a a a 1) OG(L) SIMULATED BY OG(R) 2) FOR (l,r): FORMULA(l) IMPLIES FORMULA (r)
50. DECIDE SPECIAL CASE: ~REF 15 L OG(L) R OG(R) ∅ ?a ?a τ τ τ ?a ∅ ?a τ τ ?a a a TRUE TRUE TRUE TRUE TRUE 1) OG(L) SIMULATED BY OG(R) 2) FOR (l,r): FORMULA(l) IMPLIES FORMULA (r)
51. DECIDE SPECIAL CASE: ~REF 15 L OG(L) R OG(R) ∅ ?a ?a τ τ τ ?a ∅ ?a τ τ ?a a a TRUE TRUE TRUE TRUE TRUE 1) OG(L) SIMULATED BY OG(R) 2) FOR (l,r): FORMULA(l) IMPLIES FORMULA (r)
52. OUTLINE UNIVERSE ALL SERVICES INNERLY BOUNDED SERVICES PRESERVED UNDER COMPOSITION? YES NO DECIDABLE? WITH TRACE-BASED SEMANTICS WITH OPERATING GUIDELINES DECIDE WITH OPERATING GUIDELINES? 2. B
53. OUTLINE UNIVERSE ALL SERVICES INNERLY BOUNDED SERVICES PRESERVED UNDER COMPOSITION? YES NO DECIDABLE? WITH TRACE-BASED SEMANTICS WITH OPERATING GUIDELINES DECIDE WITH OPERATING GUIDELINES? 3. B
54. DECIDE GENERAL CASE: MODIFIED ~REF 17 L OG(L) R OG(R) ∅ ?a ?a τ τ τ ?a ∅ ?a τ τ ?a a a 1) OG(L) SIMULATED BY OG(R) 2) FOR (l,r): FORMULA(l) IMPLIES FORMULA (r) 3) ∅ OF OG(L) ONLY SIMULATED BY ∅ OF OG(R)
55. DECIDE GENERAL CASE: MODIFIED ~REF 17 L OG(L) R OG(R) ∅ ?a ?a τ τ τ ?a ∅ ?a τ τ ?a a a TRUE TRUE TRUE TRUE TRUE 1) OG(L) SIMULATED BY OG(R) 2) FOR (l,r): FORMULA(l) IMPLIES FORMULA (r) 3) ∅ OF OG(L) ONLY SIMULATED BY ∅ OF OG(R)
56. DECIDE GENERAL CASE: MODIFIED ~REF 17 L OG(L) R OG(R) ∅ ?a ?a τ τ τ ?a ∅ ?a τ τ ?a a a TRUE TRUE TRUE TRUE TRUE 1) OG(L) SIMULATED BY OG(R) 2) FOR (l,r): FORMULA(l) IMPLIES FORMULA (r) 3) ∅ OF OG(L) ONLY SIMULATED BY ∅ OF OG(R)
57. DECIDE GENERAL CASE: MODIFIED ~REF 17 L OG(L) R OG(R) ∅ ?a ?a τ τ τ ?a ∅ ?a τ τ ?a a a TRUE TRUE TRUE TRUE TRUE 1) OG(L) SIMULATED BY OG(R) 2) FOR (l,r): FORMULA(l) IMPLIES FORMULA (r) 3) ∅ OF OG(L) ONLY SIMULATED BY ∅ OF OG(R)
58. TAKE HOME POINTS 18 WITH OPERATING GUIDELINES TWEAKING EXISTING ALGORITHM 1 2 WE CAN DECIDE 3 WITH/WITHOUT FINAL MARKINGS
59. TAKE HOME POINTS 18 WITH OPERATING GUIDELINES TWEAKING EXISTING ALGORITHM 1 2 FUTURE WORK + STRICTER TERMINATION CRITERIA (RESPONSIVENESS, WEAK TERMINATION, ...) WE CAN DECIDE 3 WITH/WITHOUT FINAL MARKINGS
60. richard.mueller@informatik.hu-berlin.de http://about.me/richardmueller RICHARD MÜLLER CHRISTIAN STAHL THANK YOU! L R