Approximation of CFL by Regular Languages for Concurrent Program Verification

Abstract

Many problems related to verification of concurrentprograms can be reduced to the non-empty intersectionproblem for context-free languages. Since the latter is anundecidable problem, a practical approach for solving theintersection problem is to convert it to a decidable problemof the non-empty intersection of a context-free languageand a regular language. This is done by approximatingone of the context-free languages in the intersection fromabove or from below by a regular language. We give anapproximation technique from above by modeling a context-free language L in terms of linear integer inequalitiesand then obtaining the approximating regular language L¢Ê L by relaxing the linear inequalities such that eachinequality involves at most one variable. Previous approximationtechniques focused on approximation below. Wealso give an alternate technique with a finite-state automatabased approach, where we start with an automata Mwhich accepts a suitable finite-subset L0 of L, and thenextend M successively based on the pumping property ofL till the language accepted by M contains L