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Mobile Calculi

Mobile Calculi. Prof. Diletta Romana Cacciagrano. Operational Semantics based on reduction. Reduction semantics. Reduction semantics. :. ( red-cong ). Alpha-conversion. Structural congruence. Structural congruence. Operational Semantics based on labels.

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Mobile Calculi

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  1. Mobile Calculi Prof. Diletta Romana Cacciagrano

  2. OperationalSemanticsbased on reduction

  3. Reductionsemantics

  4. Reductionsemantics : (red-cong)

  5. Alpha-conversion

  6. Structuralcongruence

  7. Structuralcongruence

  8. OperationalSemanticsbased on labels

  9. Labeledsemantics (Lateoperationalsemantics)

  10. Labeledsemantics(Lateoperational) semantics+alphaconv

  11. Labeledsemantics(Lateoperationalsemantics+alphaconv +structcong) α CONG α

  12. Labeledsemantics (Earlyoperationalsemantics)

  13. Labeledsemantics(Earlyoperationalsemantics+alphaconv)

  14. Labeledsemantics(Earlyoperationalsemantics+alphaconv +structcong) α CONG α

  15. Labeledsemantics

  16. Labeledsemantics

  17. Labeledsemantics Early and late LTSs

  18. Reduction and Labeledsemantics

  19. OperationalEquivalencesbased on labels

  20. Bisimulation

  21. Bisimulation on Pi-calculus

  22. Strong late bisimulation L

  23. Strong late bisimulation L

  24. Strong earlybisimulation(finerthan late)

  25. Late Instantiation

  26. EarlyInstantiation

  27. Input L

  28. Congruence

  29. Congruencew.r.t.parallel(proofforearly. Similarlyfor late) Theorem:

  30. Congruencew.r.t.parallel (proofforearly. Similarlyfor late)

  31. Congruencew.r.t.parallel (proofforearly. Similarlyfor late)

  32. Substitutionpreservation

  33. Strong bisimilarityisnot a congruence(proofforearly. Similarlyfor late))

  34. Open bisimulation(Bisimulationfor Pi) Nameinstantationismoved inside the definitionofbisimulation. The open bisimilarity, written , is the largest open bisimulation.

  35. Open bisimilarity(Full bisimilarity)

  36. OperationalEquivalencesbased on reduction:TestingPreorders

  37. Testingmachinery A set ofprocessestobe test. A set oftests or observers. These are obtainedbyextending the syntaxofprocessesto generate processeswhich can perform a particularaction (omega) reporting success. A way toexercise a process on a given test: itisdonebyletting the process and the test torun in parallel and bylooking at the computationswhich the embeddedprocess can perform. Thesecomputations can besuccessful or failing, depending on whether or nottheyallow the executionof omega. A generalcriterion (semantics) forinterpreting the resultsoftheseexercises.

  38. Testingmachinery Observer (Tests) Experiments

  39. Maximal computations

  40. May Testing

  41. MustTesting

  42. Fair Testing

  43. Testingpreorders

  44. Testing and Bisimulationequivalences Bisimulationequivalences are usuallyratherstrict: theydepend on the whole branching structureofprocesseswhich, in some cases, are notrelevant. Weak bisimulation incorporates a particular notion of fairness: it abstracts from the tau-loops (i.e infinite sequences of tau-moves): the “normal” behavior can be resumed each time after a finite sequence of tau-moves. Must testing semantics is based on the interpretation of tau-loops as divergences, making them quasi-observable as a chaotic or under-specified behavior. Forthis, ithasbeendefinedfair-testingsemantics. The standard testing equivalences are coarser than weak bisimulation in the case of divergence-free processes, and they are incomparable in general.

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