Fair Π

AbstractIn this paper, we define fair computations in the π-calculus [Milner, R., Parrow, J. & Walker, D., A Calculus of Mobile Processes, Part I and II, Information and Computation 100 (1992) 1–78]. We follow Costa and Stirling's approach for CCS-like languages [Costa, G. & Stirling, C., A Fair Calculus of Communicating Systems, Acta Informatica 21 (1984) 417–441, Costa, G. & Stirling, C., Weak and Strong Fairness in CCS, Information and Computation 73 (1987) 207–244] but exploit a more natural labeling method of process actions to filter out unfair process executions. The new labeling allows us to prove all the significant properties of the original one, such as unicity, persistence and disappearance of labels. It also turns out that the labeled π-calculus is a conservative extension of the standard one. We contrast the existing fair testing [Brinksma, E., Rensink, A. & Vogler, W., Fair Testing, Proc. of CONCUR'95, LNCS, 962 (1995) 313–327, Natarajan, V. & Cleaveland, R., Divergence and Fair Testing, Proc. of ICALP '95, LNCS, 944 (1995) 648–659] with those that naturally arise by imposing weak and strong fairness as defined by Costa and Stirling. This comparison provides the expressiveness of the various fair testing-based semantics and emphasizes the discriminating power of the one already proposed in the literature

The language of certain conflicts of a nondeterministic process

The language of certain conflicts is the most general set of behaviours of a nondeterministic process, which certainly lead to a livelock or deadlock when accepted by another process running in parallel. It is of great use in model checking to detect livelocks or deadlocks in very large systems, and in process-algebra to obtain abstractions preserving livelock and deadlock. Unfortunately, the language of certain conflicts is difficult to compute and has only been approximated in previous work. This paper presents an effective algorithm to calculate the language of certain conflicts for any given nondeterministic finite-state process and discusses its properties. The algorithm is shown to be correct and of exponential complexity

Full abstraction for fair testing in CCS

In previous work with Pous, we defined a semantics for CCS which may both be viewed as an innocent presheaf semantics and as a concurrent game semantics. It is here proved that a behavioural equivalence induced by this semantics on CCS processes is fully abstract for fair testing equivalence. The proof relies on a new algebraic notion called playground, which represents the 'rule of the game'. From any playground, two languages, equipped with labelled transition systems, are derived, as well as a strong, functional bisimulation between them.Comment: 15 pages, to appear in CALCO '13. To appear Lecture notes in computer science (2013

Explicit fairness in testing semantics

In this paper we investigate fair computations in the pi-calculus. Following Costa and Stirling's approach for CCS-like languages, we consider a method to label process actions in order to filter out unfair computations. We contrast the existing fair-testing notion with those that naturally arise by imposing weak and strong fairness. This comparison provides insight about the expressiveness of the various `fair' testing semantics and about their discriminating power.Comment: 27 pages, 1 figure, appeared in LMC

Conformance Testing with Labelled Transition Systems: Implementation Relations and Test Generation

This paper studies testing based on labelled transition systems, presenting two test generation algorithms with their corresponding implementation relations. The first algorithm assumes that implementations communicate with their environment via symmetric, synchronous interactions. It is based on the theory of testing equivalence and preorder, as is most of the testing theory for labelled transition systems, and it is found in the literature in some slightly different variations. The second algorithm is based on the assumption that implementations communicate with their environment via inputs and outputs. Such implementations are formalized by restricting the class of labelled transition systems to those systems that can always accept input actions. For these implementations a testing theory is developed, analogous to the theory of testing equivalence and preorder. It consists of implementation relations formalizing the notion of conformance of these implementations with respect to labelled transition system specifications, test cases and test suites, test execution, the notion of passing a test suite, and the test generation algorithm, which is proved to produce sound test suites for one of the implementation relations

On the Representation of McCarthy's amb in the π-calculus

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Structural Rewriting in the pi-Calculus

We consider reduction in the synchronous pi-calculus with replication, without sums. Usual definitions of reduction in the pi-calculus use a closure w.r.t. structural congruence of processes. In this paper we operationalize structural congruence by providing a reduction relation for pi-processes which also performs necessary structural conversions explicitly by rewrite rules. As we show, a subset of structural congruence axioms is sufficient. We show that our rewrite strategy is equivalent to the usual strategy including structural congruence w.r.t.the observation of barbs and thus w.r.t. may- and should-testing equivalence in the pi-calculus