Algorithmic verification of linear temporal logic specifications

Abstract

In this methodological paper we present a coherent framework for symbolic model checking verification of linear-time temporal logic (LTL) properties of reactive systems, taking full fairness into consideration. We use the computational model of a fair Kripke structure (FKS) which takes into account both justice (weak fairness) and compassion (strong fairness). The approach presented here reduces the model checking problem into the question of whether a given FKS is feasible (i.e. has at least one computation). The contribution of the paper is twofold: On the methodological level, it presents a direct self-contained exposition of full LTL symbolic model checking without resorting to reductions to either CTL or automata. On the technical level, it extends previous methods by dealing with compassion at the algorithmic level instead of adding it to the specification, and providing the first symbolic method for checking feasibility of FKS's (equivalently, symbolically checking for the emptiness of Streett automata). The presented algorithms can also be used (with minor modifications) for symbolic model-checking of CTL formulas over fair Kripke structures with compassion requirements.