Model-checking of infinite graphs defined by graph grammars

We propose here an algorithm that decides whether a state of an innnite graph deened by a graph grammar satisses a given formula of the alternation-free-calculus. We rst show how graph grammars enable to nitely represent innnite transition systems. In particular, a connection is made between a state of the graph grammar and the states of the innnite graph it represents. We then present succinctly the syntax and the standard semantics of the-calculus. A non-standard semantics, called assertion-based semantics is then proposed. That semantics makes possible to reduce the study of the semantics of an innnite graph to parts of that graph by using correct assertions. Our algorithm then determines transformers, for each state of the graph grammar, which, given the context, expressed by an assertion, of a state of the graph represented by a state of the graph grammar, decides whether a given formula is satissed by that state of the graph, or not. Model-Checking de graphes innnis d eenis par des grammaires de graphe R esum e : Nous pr esentons ici un algorithme qui d ecide si un etat d'un graphe innni d eeni par une grammaire de graphe v eriie une formule donn ee du-calcul sans alternation de point xe. Nous montrons d'abord comment les grammaires de graphe permettent de repr esenter de mani ere nie des syst emes de transition innnis. En particulier, un lien est etabli entre un etat de la grammaire de graphe et les etats du graphe innni qu'il repr esente. Nous pr esentons alors succinctement la syntaxe et la s emantique standard du-calcul. Une s emantique non-standard, dite fond ee sur des assertions, est ensuite propos ee. Cette s emantique rend possible de r eduire l' etude de la s emantique d'un graphe innni a des parties de ce graphe en utilisant des assertions correctes. Notre algorithme d etermine alors des transformateurs,