Model-Checking of Infinite Graphs Defined by Graph Grammars

Abstract

In 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.