Model Checking for Context-Free Processes

We develop a model-checking algorithm that decides for a given context-free process whether it satisfies a property written in the alternation-free modal mu-calculus. The central idea behind this algorithm is to raise the standard iterative model-checking techniques to higher order: in contrast to the usual approaches, in which the set of formulas that are satisfied by a certain state are iteratively computed, our algorithm iteratively computes a property transformer for each state class of the finite process representation. These property transformers can then simply be applied to solve the model-checking problem. The complexity of our algorithm is linear in the size of the system's representation and exponential in the size of the property being investigated

More Infinite Results

Recently there has been a spurt of activity in concurrency theory centred on the analysis of infinite-state systems. The following two problems have been intensely investigated: (1) given two infinite-state systems, are they equal with respect to a certain equivalence notion?, and (2) given an infinite-state system and a property expressed in a certain temporal logic, does the system satisfy the property? In his paper "Infinite Results" [Mol96] , Moller surveys some of the key results on the decidability and complexity of problem (1). This paper is a survey on the results about problem (2). 1 Introduction Most techniques for the verification of concurrent systems proceed by an exhaustive traversal of the state space. Therefore, they are inherently incapable of considering systems with infinitely many states. Recently, some methods have been developed to overcome this limitation, at least for restricted classes of infinite-state systems. Using them, several verification problems have b..

Model-Checking of Infinite Graphs Defined by Graph Grammars

AbstractIn this paper, we consider the model-checking problem for regular graphs, i.e. infinite transition graphs defined in terms of deterministic graph grammars. It turns out that an elegant adaptation of the model-checker for pushdown processes leads to an algorithm that decides whether the root of a regular graph under consideration satisfies a given formula of the alternation-free modal μ-calculus. The key to the algorithm is to exploit the underlying structure of regular graphs, as well as to consider a variant of standard μ-calculus semantics, called the assertion-based semantics, which allow to presume the validity of formulas at distinguished states

Boolean algebras by length recognizability

International audienceWe present a simple approach to define Boolean algebras on languages. We proceed by inverse deterministic and length-preserving morphisms on automata whose vertices are words. We give applications for context-free languages and context-sensitive languages