The Regular Viewpoint on PA-Processes

PA is the process algebra allowing non-determinism, sequential and parallel compositions, and recursion. We suggest a view of PA-processes as {\em tree languages}. Our main result is that the set of iterated predecessors of a regular set of PA-processes is a regular tree language, and similarly for iterated successors. Furthermore, the corresponding tree-automata can be built effectively in polynomial-time. This has many immediate applications to verification problems for PA-processes, among which a simple and general model-checking algorithm

A regular viewpoint on processes and algebra

While different algebraic structures have been proposed for the treatment of concurrency, finding solutions for equations over these structures needs to be worked on further. This article is a survey of process algebra from a very narrow viewpoint, that of finite automata and regular languages. What have automata theorists learnt from process algebra about finite state concurrency? The title is stolen from [31]. There is a recent survey article [7] on finite state processes which deals extensively with rational expressions. The aim of the present article is different. How do standard notions such as Petri nets, Mazurkiewicz trace languages and Zielonka automata fare in the world of process algebra? This article has no original results, and the attempt is to raise questions rather than answer them

Transitive Closures of Semi-commutation Relations on Regular omega-Languages

A semi-commutation $R$ is a relation on a finite alphabet $A$. Given an infinite word $u$ on $A$, we denote by $R(u)=\{xbay\mid x\in A^*,y\in A^\omega \ (a,b)\in R \text{ and } xaby=u\}$ and by $R^*(u)$ the language $\{u\}\cup \cup_{k\geq 1} R^k(u)$. In this paper we prove that if an $\omega$-language $L$ is a finite union of languages of the form $A_0^*a_1A_1^*\ldots a_k A_k^*a_{k+1}A_{k+1}^*$, where the $A_i$'s are subsets of the alphabet and the $a_i$'s are letters, then $R^*(L)$ is a computable regular $\omega$-language accepting a similar decomposition. In addition we prove the same result holds for $\omega$-languages which are finite unions of languages of the form $L_0a_1L_1\ldots a_k L_ka_{k+1}L_{k+1}$, where the $L_i$'s are accepted by diamond automata and the $a_i$'s are letters. These results improve recent works by Bouajjani, Muscholl and Touili on one hand, and by Cécé, Héam and Mainier on the other hand, by extending them to infinite words

Rewriting in the partial algebra of typed terms modulo AC

AbstractWe study the partial algebra of typed terms with an associative commutative and idempotent operator (typed AC-terms). The originality lies in the representation of the typing policy by a graph which has a decidable monadic theory.In this paper we show on two examples that some results on AC-terms can be raised to the level of typed AC-terms. The examples are the results on rational languages (in particular their closure by complement) and the property reachability problem for ground rewrite systems (equivalently process rewrite systems)

Regular hedge model checking

We extend the regular model checking framework so that it can handle systems with arbitrary width tree-like structures. Con gurations of a system are represented by trees of arbitrary arities, sets of con gurations are represented by regular hedge automata, and the dynamics of a system is modeled by a regular hedge transducer. We consider the problem of computing the transitive closure T + of a regular hedge transducer T. This construction is not possible in general. Therefore, we present a general acceleration technique for computing T+. Our method consists of enhancing the termination of the iterative computation of the different compositions Ti by merging the states of the hedge transducers according to an appropriate equivalence relation that preserves the traces of the transducers. We provide a methodology for effectively deriving equivalence relations that are appropriate. We have successfully applied our technique to compute transitive closures for some mutual exclusion protocols de ned on arbitrary width tree topologies, as well as for an XML application.4th IFIP International Conference on Theoretical Computer ScienceRed de Universidades con Carreras en Informática (RedUNCI

Context-Bounded Analysis For Concurrent Programs With Dynamic Creation of Threads

Context-bounded analysis has been shown to be both efficient and effective at finding bugs in concurrent programs. According to its original definition, context-bounded analysis explores all behaviors of a concurrent program up to some fixed number of context switches between threads. This definition is inadequate for programs that create threads dynamically because bounding the number of context switches in a computation also bounds the number of threads involved in the computation. In this paper, we propose a more general definition of context-bounded analysis useful for programs with dynamic thread creation. The idea is to bound the number of context switches for each thread instead of bounding the number of switches of all threads. We consider several variants based on this new definition, and we establish decidability and complexity results for the analysis induced by them

Constrained Dynamic Tree Networks

We generalise Constrained Dynamic Pushdown Networks, introduced by Bouajjani\et al, to Constrained Dynamic Tree Networks.<br>In this model, we have trees of processes which may monitor their children.<br>We allow the processes to be defined by any computation model for which the alternating reachability problem is decidable.<br>We address the problem of symbolic reachability analysis for this model. More precisely, we consider the problem of computing an effective representation of their reachability<br>sets using finite state automata. <div>We show that backwards reachability sets starting from regular sets of configurations are always regular. </div><div>We provide an algorithm for computing backwards reachability sets using tree automata.<br><br></div