Free submonoids and minimal ω-generators of Rω

Let A be an alphabet and let R be a language in A+. An (¿-generator of -R" is a language G such that G" = R". The language Stab(-R") = {u G A* : ttiZ" Ç R"} is a submonoid of A*. We give results concerning the wgenerators for the case when Stab(Ru ) is a free submonoid which are not available in the general case. In particular, we prove that every ((»-generator of 22" contains at least one minimal w-generator of R". Furthermore these minimal w-generators are codes. We also characterize the w-languagea having only finite languages as minimal u-generators. Finally, we characterize the w- languages »-generated by finite prefix codes

A Decidable Characterization of a Graphical Pi-calculus with Iterators

This paper presents the Pi-graphs, a visual paradigm for the modelling and verification of mobile systems. The language is a graphical variant of the Pi-calculus with iterators to express non-terminating behaviors. The operational semantics of Pi-graphs use ground notions of labelled transition and bisimulation, which means standard verification techniques can be applied. We show that bisimilarity is decidable for the proposed semantics, a result obtained thanks to an original notion of causal clock as well as the automatic garbage collection of unused names.Comment: In Proceedings INFINITY 2010, arXiv:1010.611

Finite acceptance of infinite words

AbstractIn this paper we consider the following two types of finite acceptance of infinite words by finite automata: An infinite word ξ is accepted if and only if there is a run on input ξ for which 1.(1) an accepting state is visited at least once, or2.(2) an accepting state is visited at least once but only finitely often. The resulting classes of regular ω-languages are characterized by language-theoretic means, and they are positioned into the known hierarchies of regular ω-languages

Computing with graph rewriting systems with priorities

AbstractIn this paper, the computational power of the noetherian graph rewriting systems with priorities (PGRSs) is studied. We define the notion of safe PGRS with respect to a given property. The PGRSs are considered as recognizers for sets of graphs (1-graphs). The classes of sets of graphs (1-graphs) so defined are compared with the classes definable by logic formulas. We end with the particular cases of trees and words

Des algorithmes autour des codes rationnels

Dans cette thèse, nous nous intéressons au problème de décider si un langage rationnel donné est un omega-code. Nous décrivons donc des algorithmes pour décider de cette propriété dans le cas des langages finis et dans le cas rationnel. Ces travaux nous ont permis de mettre en évidence des langages tels que leurs puissances oméga contiennent des mots infinis qui ont plusieurs factorisations, et que celles-ci ne soient que des puissances oméga de factorisations de mots finis avec plusieurs factorisations (les pré-oméga-codes). Nous avons étudié quelques propriétés de ces pré-oméga-codes en rapport avec les générateurs de langages de mots infinis. Enfin, l'étude des factorisations des mots (finis ou infinis) dans le cadre précédent, nous a amené à nous intéresser à une notion de factorisation généralisée pour des mots engendrés par plusieurs langages. La construction d'un tel mot est dirigée'' par un mot (appelé trajectoire) issu d'un langage de contrôle. Nous avons étudié la notion de code associé et définit une notion de stabilité.In this thesis, we are interested in deciding if a given rational language is a -codes. Thus, we describe algorithms to decide this property in the case of finite languages and rational ones. This work enabled us to put in obviousness the languages whose power- contain infinite words which have several factorizations (the pre- -codes). We studied some properties of these pre- -codes in connection with the generators of languages of infinite words. Lastly, the study of factorizations of words (finite or infinite) within the preceding framework, led us to study a concept of generalized factorization for words of languages generated by two languages, and whose construction is directed by a word (called trajectory) resulting from a language of control. We studied the notion of associated code and defined a concept of stability.NICE-BU Sciences (060882101) / SudocSudocFranceF