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Mobile Calculi

Mobile Calculi. Prof. Diletta Romana Cacciagrano. Some expressiveness results. Expressiveness. In general, in order to compare the expressive power of two languages, we look for the existence/non existence of an encoding with certain properties among these languages.

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Mobile Calculi

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  1. Mobile Calculi Prof. Diletta Romana Cacciagrano

  2. Some expressivenessresults

  3. Expressiveness In general, in order to compare the expressive power of two languages, we look for the existence/non existence of an encoding with certain properties among these languages. What is a good notion of encoding to be used as a basis to measure the relative expressive power? In general we would be happy with an encoding L1L2 being:

  4. A goodnotionofencoding Compositional w.r.t. the operators (Preferably) homomorphicw.r.t. parallel (distribution-preserving)

  5. A goodnotionofencoding • Preserving some kind of semantics. Here there are several possibilities: • Preserving observables • Preserving equivalence (This is one of the most popular requirements for an encoding)

  6. A goodnotionofencoding (Preferably) the encoding should not introduce divergences (tau-loops), in the sense that if in the original process all the computations converge, then the same holds for its translation. Note that weak bisimulations are insensitive w.r.t. divergences.

  7. Expressiveness: Processmobilityasnamemobility

  8. Expressiveness: Processmobilityasnamemobility

  9. Expressiveness: Polyadicasmonadic

  10. Expressiveness: Replication vs recursion

  11. Expressiveness: Replication vs recursion Theorem: |

  12. Expressiveness: Data (Boolean) asprocesses | * | |

  13. Expressiveness: Synchronyasasynchrony(Boudol’s Encoding) Boudol (1992) provided the following encoding of Pi (without choice) into asynchronous Pi. The idea is to force both partners to proceed only when it is sure that the communication can take place, by using a sort of rendez-vous protocol.

  14. Expressiveness: Synchronyasasynchrony(Boudol’s Encoding)

  15. Expressiveness: Synchronyasasynchrony(Honda and Tokoro’s Encoding) Honda-Tokoro (1992) defined the following encoding of Pi (without choice) into asynchronous Pi, in which the communication protocol takes two steps instead than three. The idea is to let the receiver take the initiative (instead than the sender).

  16. Expressiveness: Synchronyasasynchrony(Honda and Tokoro’s Encoding)

  17. Expressiveness: Synchronyasasynchrony(Honda and Tokoro’s Encoding) Honda proved this encoding sound and “almost” complete w.r.t. a certain logical semantics.

  18. Expressiveness: Synchronyasasynchrony and Testingsemantics We don’t expect the encodings the encodings of output prefix to be correct w.r.t. testing semantics (why?) but we would like the encoding to satisfy at least the following property: where can be

  19. Expressiveness: Synchronyasasynchrony and Testingsemantics The encoding of Boudol and Honda-Tokoro preserve may and fair semantics, but not must semantics, i.e.

  20. Expressiveness: Synchronyasasynchrony and Testingsemantics • Theorem[Cacciagrano, Corradini, Palamidessi, 2004]: • Let an encoding of Pi-calculus (without choice) into asynchronous Pi-calculus such that • compositional w.r.t. prefixes • there exists P such that P diverges • Then does not preserve must testing.

  21. Expressiveness: Synchronyasasynchrony and Testingsemantics • The problem, however, is uniquely a problem of fairness. • Theorem[Cacciagrano, Corradini, Palamidessi, 2004]: • The encodings of Boudol and of Honda-Tokoro • preserve must testing if we restrict to fair computations only. • preserve a version of must testing called fair-must testing.

  22. The Pi-calculushierarchy

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