Section: New Results

Verification techniques for extensional properties

Participants : Daniel Hirschkoff, Elena Giachino, Michael Lienhardt, Cosimo Laneve, Jean-Marie Madiot, Davide Sangiorgi.

Extensional refers to properties that have to do with behavioural descriptions of a system (i.e., how a system looks like from the outside). Examples of such properties include classical functional correctness and deadlock freedom. Related to techniques for extensional properties are the issues of decidability (the problem of establishing whether certain properties are computationally feasable).

Coinductive techniques

Coinductive techniques, notably those based on bisimulation, are widely used in concurrency theory to reason about systems of processes. The bisimulation proof method can be enhanced by employing 'bisimulations up-to' techniques. A comprehensive theory of such enhancements has been developed for first-order (i.e., CCS-like) LTSs and bisimilarity, based on the notion of compatible function for fixed-point theory. We have transported this theory onto languages whose bisimilarity and LTS go beyond those of first-order models [40] . The approach consists in exhibiting fully abstract translations of the more sophisticated LTSs and bisimilarities onto the first-order ones. This allows us to reuse directly the large corpus of up-to techniques that are available on first-order LTSs. We have investigated the method on the $\pi$-calculus, the Higher-Order $\pi$-calculus, and a (call-by-value) $\lambda$-calculus with references.

In [20] , mostly a tutorial paper, a few forms of bisimulation and of coinductive techniques that have been proposed for higher-order languages are discussed, beginning with the pure lambda-calculus and then moving to extensions of it, notably those with non-determinism and probabilities.

Deadlock detection

Deadlock detection in concurrent programs that create networks with an arbitrary number of nodes is extremely complex and solutions either give imprecise answers or do not scale. To enable the analysis of such programs, we have studied an algorithm for detecting deadlocks [37] , [35] , in a basic model featuring recursion and fresh name generation, called Lam. We then have designed a type system that associates Lams to processes. As a byproduct of these two techniques, we have an algorithm that is more powerful than previous ones and that can be easily integrated into the current release of TyPiCal, a type-based analyser for $\pi$-calculus.

Expressiveness and decidability in actor-like systems

Refining work in previous years, we have studied [15] the expressive power of an actor-like language, featuring concurrent objects and asynchronous message-passing. We have identified the presence/absence of fields as a crucial feature: the dynamic creation of names in combination with fields gives rise to Turing completeness. On the other hand, restricting to stateless actors gives rise to systems for which properties such as termination are decidable. This decidability result still holds for actors with states when the number of actors is bounded and the state is read-only.