Abstract

We apply the symbolic analysis principle to pushdown systems. We represent (possibly infinite) sets of configurations of such systems by means of finite-state automata. In order to reason in a uniform way about analysis problems involving both existential and universal path quantification (like model-checking for branching-time logics), we consider the more general class of alternating pushdown systems and use alternating finite-state automata as a representation structure for their sets of configurations. We give a simple and natural procedure to compute sets of predecessors for this representation structure. We apply this procedure and the automata-theoretic approach to model-checking to define new model-checking algorithms for pushdown systems and both linear and branching-time properties. From these results we derive upper bounds for several model-checking problems, and we also provide matching lower bounds, using reductions based on some techniques introduced by Walukiewicz.

Citations