Section: New Results

Expressiveness of computational models

Participants : Mila Dalla Preda, Ugo Dal Lago, Ivan Lanese, Cosimo Laneve, Davide Sangiorgi.

Expressiveness refers to the study of the expressive power of computational models. In 2011 we have addressed four main aspects.

First, we have continued our investigation of reversible computations. Reversibility is a main ingredient in the study of programming abstractions for reliable systems, e.g. for exception handling. In fact, reversibility can be used for going back to some consistent state after an exception has occurred. In previous years we had defined $\rho \pi$, a higher-order calculus where processes can both go forward and backward in the computation. This year we have studied [33] fine-grained rollback primitives to control reversibility. The definition of a proper semantics for such a primitive is a surprisingly delicate matter because of the potential interferences between concurrent rollbacks. We have also considered lower-level distributed semantics, which are closer to an actual implementation of the rollback primitives, and their relationship with the high-level semantics.

A thread of research close to that of $\rho \pi$ is the study of the properties and the expressive power of a simple calculus with reversible transitions, called reversible structures. In [24] , we have demonstrated a standardization theorem for these structures. When terms in reversible structures have unique id, the standardization theorem may be strengthened in a form that bears a quadratic algorithm for reachability, a problem that is EXPSPACE-complete for generic structures (as in Petri Nets). The expressive power of reversible structures has been studied in [17] , [12] and a compilation of asynchronous Reversible CCS has been provided.

A second aspect has been been motivated by the analogy between malicious software and biological infections [39] . In the paper, we have used a formalism originally developed for the analysis of biological systems — the kappa calculus by Danos and Laneve — for the formalization and analysis of malicious software. In particular we have modeled the different actors involved in a malicious code attack in the kappa-calculus. Then, by simulating the behavior, we have shown how to extract relevant information that can drive the choice of the defense technique to apply.

A third aspect has been the refinement [14] of some previous work on the expressiveness and decidability of higher-order concurrent languages. — formalisms for concurrency in which processes can be passed around in communications.

A fourth aspect has been the study of properties of a simple calculus for quantum computation. In [16] , we have demonstrated a confluence property both for finite and infinite computations using a novel technique.