A Distribution Law for CCS and a New Congruence Result for the pi-calculus

We give an axiomatisation of strong bisimilarity on a small fragment of CCS that does not feature the sum operator. This axiomatisation is then used to derive congruence of strong bisimilarity in the finite pi-calculus in absence of sum. To our knowledge, this is the only nontrivial subcalculus of the pi-calculus that includes the full output prefix and for which strong bisimilarity is a congruence.Comment: 20 page

Decidability of Identity-free Relational Kleene Lattices

National audienceFamilies of binary relations are important interpretations of regular expressions, and the equivalence of two regular expressions with respect to their relational interpretations is decidable: the problem reduces to the equality of the denoted regular languages.Putting together a few results from the literature, we first make explicit a generalisation of this reduction, for regular expressions extended with converse and intersection: instead of considering sets of words (i.e., formal languages), one has to consider sets of directed and labelled graphs.We then focus on identity-free regular expressions with intersection—a setting where the above graphs are acyclic—and we show that the corresponding equational theory is decidable. We achieve this by defining an automaton model, based on Petri Nets, to recognise these sets of acyclic graphs, and by providing an algorithm to compare such automata

De la KAM avec un Processus d'Ordre Supérieur

National audienceNous présentons un encodage simple et direct de la machine abstraite de Krivine (KAM) dans le calcul de processus d'ordre supérieur HOcore, en utilisant un nombre très restreint de canaux de communication. Cet encodage montre qu'il est possible de capturer l'expressivité du lambda-calcul en HOcore dès que l'on fixe l'ordre d'évaluation. Nous donnons également une nouvelle borne inférieure pour le nombre minimal de restrictions nécessaire pour rendre l'équivalence de programmes dans HOcore indécidable

Treewidth-Two Graphs as a Free Algebra

We give a new and elementary proof that the graphs of treewidth at most two can be seen as a free algebra. This result was originally established through an elaborate analysis of the structure of K_4-free graphs, ultimately reproving the well-known fact that the graphs of treewidth at most two are precisely those excluding K_4 as a minor. Our new proof is based on a confluent and terminating rewriting system for term-labeled graphs and does not involve graph minors anymore. The new strategy is simpler and robust in the sense that it can be adapted to subclasses of treewidth-two graphs, e.g., graphs without self-loops

Completeness for Identity-free Kleene Lattices

We provide a finite set of axioms for identity-free Kleene lattices, which we prove sound and complete for the equational theory of their relational models. Our proof builds on the completeness theorem for Kleene algebra, and on a novel automata construction that makes it possible to extract axiomatic proofs using a Kleene-like algorithm

Non Axiomatisability of Positive Relation Algebras with Constants, via Graph Homomorphisms

We study the equational theories of composition and intersection on binary relations, with or without their associated neutral elements (identity and full relation). Without these constants, the equational theory coincides with that of semilattice-ordered semigroups. We show that the equational theory is no longer finitely based when adding one or the other constant, refuting a conjecture from the literature. Our proofs exploit a characterisation in terms of graphs and homomorphisms, which we show how to adapt in order to capture standard equational theories over the considered signatures

Formal verification in Coq of program properties involving the global state effect

The syntax of an imperative language does not mention explicitly the state, while its denotational semantics has to mention it. In this paper we present a framework for the verification in Coq of properties of programs manipulating the global state effect. These properties are expressed in a proof system which is close to the syntax, as in effect systems, in the sense that the state does not appear explicitly in the type of expressions which manipulate it. Rather, the state appears via decorations added to terms and to equations. In this system, proofs of programs thus present two aspects: properties can be verified {\em up to effects} or the effects can be taken into account. The design of our Coq library consequently reflects these two aspects: our framework is centered around the construction of two inductive and dependent types, one for terms up to effects and one for the manipulation of decorations

Cyclic Proofs and Jumping Automata

We consider a fragment of a cyclic sequent proof system for Kleene algebra, and we see it as a computational device for recognising languages of words. The starting proof system is linear and we show that it captures precisely the regular languages. When adding the standard contraction rule, the expressivity raises significantly; we characterise the corresponding class of languages using a new notion of multi-head finite automata, where heads can jump