Upgrade to Pro — share decks privately, control downloads, hide ads and more …

Deciding The Precongruence For Deadlock Freedom...

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.

Richard Müller

June 26, 2012
Tweet

More Decks by Richard Müller

Other Decks in Research

Transcript

  1. RICHARD MÜLLER CHRISTIAN STAHL L R DECIDING THE PRECONGRUENCE FOR

    DEADLOCK FREEDOM USING OPERATING GUIDELINES
  2. SERVICE SETTING 2 A L SERVICE SERVICE A⊕L COMPOSITION DEF:

    CONTROLLER A CONTROLS L IFF A⊕L IS DEADLOCK FREE AND BOUNDED
  3. SERVICE SUBSTITUTION 3 L R ⊆ DEF: ACCORDANCE R ACCORDS

    WITH L IFF FOR ALL A: A CONTROLS L IMPLIES A CONTROLS R
  4. 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
  5. 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
  6. 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
  7. 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
  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 DECIDE WITH OPERATING GUIDELINES? B
  9. 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
  10. 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
  11. 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
  12. 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
  13. 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
  14. 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
  15. 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
  16. 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
  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 CONT⊆UxU U UB CONT⊆UBxUB ACC ⊆UxU ACC ⊆UBxUB SPECIAL CASE: RESTRICTS CONTROLLER AND ACCORDANCE
  18. 8 A L GENERAL CASE: A CONTROLS L AND R

    INFLUENCES OF THE UNIVERSE R SPECIAL CASE: A CONTROLS L AND R
  19. 9 B GENERAL CASE: B CONTROLS L B DOES NOT

    CONTROL R INFLUENCES OF THE UNIVERSE L R SPECIAL CASE: B NOT CONSIDERED
  20. 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
  21. 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
  22. 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
  23. OPERATING GUIDELINE 12 R OG(R) ?a ?a τ τ τ

    ?a a VIEWPOINT OF CONTROLLER
  24. OPERATING GUIDELINE 12 R OG(R) ?a ?a τ τ τ

    ?a a ∅ EMPTY NODE ENCODES UNREACHABLE BEHAVIOR
  25. OPERATING GUIDELINE 12 R OG(R) ?a ?a τ τ τ

    ?a a A a ?a BEH(A) τ ∅ EMPTY NODE ENCODES UNREACHABLE BEHAVIOR
  26. 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
  27. 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
  28. 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
  29. 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
  30. 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)
  31. 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)
  32. 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)
  33. 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)
  34. 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)
  35. 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)
  36. 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
  37. 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
  38. 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)
  39. 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)
  40. 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)
  41. 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)
  42. TAKE HOME POINTS 18 WITH OPERATING GUIDELINES TWEAKING EXISTING ALGORITHM

    1 2 WE CAN DECIDE 3 WITH/WITHOUT FINAL MARKINGS
  43. 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