Post on 02-Jan-2016
description
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
Labeled semantics (Late operational
semantics)
Labeled semantics (Late operational) semantics+alpha conv
Labeled semantics (Late operational semantics+alpha conv
+struct cong)
α
αCONG
Labeled semantics (Early operational
semantics)
Labeled semantics (Early operational semantics+alpha conv)
Labeled semantics (Early operational semantics+alpha conv
+struct cong)
α
αCONG
Labeled semantics
Labeled semantics
Labeled semantics
Early and late LTSs
Reduction and Labeled semantics
Operational Equivalencesbased on labels
Bisimulation
Bisimulation on Pi-calculus
Strong late bisimulation
L
Strong late bisimulation
L
Late Instantiation
Strong early bisimulation(finer than late)
Early Instantiation
Input
L
Congruence
Congruence w.r.t. parallel(proof for early. Similarly for late)
Theorem:
Congruence w.r.t. parallel
(proof for early. Similarly for late)
Congruence w.r.t. parallel (proof for early. Similarly for late)
Substitution preservation
Strong bisimilarity is not a congruence(proof for early. Similarly for late))
Open bisimulation(Bisimulation for Pi)
Name instantation is moved inside the definition of bisimulation.
The open bisimilarity, written , is the largest open bisimulation.
Open bisimilarity (Full bisimilarity)
Operational Equivalencesbased on reduction:Testing Preorders
Testing machinery
A set of processes to be test.
A set of tests or observers. These are obtained by extending the syntax of processes to generate processes which can perform a particular action (omega) reporting success.
A way to exercise a process on a given test: it is done by letting the process and the test to run in parallel and by looking at the computations which the embedded process can perform. These computations can be successful or failing, depending on whether or not they allow the execution of omega.
A general criterion (semantics) for interpreting the results of these exercises.
Testing machinery
Observer (Tests)
Experiments
Maximal computations
May Testing
Must Testing
Fair Testing
Testing preorders
Testing and Bisimulation equivalences
Bisimulation equivalences are usually rather strict: they depend on the whole branching structure of processes which, in some cases, are not relevant.
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. For this, it has been defined fair-testing semantics.
The standard testing equivalences are coarser than weak bisimulation in the case of divergence-free processes, and they are incomparable in general.