Combination Methods for Satisfiability and Model-Checking of Infinite-State Systems

Abstract

Manna and Pnueli have extensively shown how a mixture of first-order logic (FOL) and discrete Linear time Temporal Logic (LTL) is sufficient to precisely state verification problems for the class of reactive systems. Theories in FOL model the (possibly infinite) data structures used by a reactive system while LTL specifies its (dynamic) behavior. In this paper, we derive undecidability and decidability results for both the satisfiability of (quantifier-free) formulae and the model-checking of safety properties by lifting combination methods for (non-disjoint) theories in FOL. The proofs of our decidability results suggest how decision procedures for the constraint satisfiability problem of theories in FOL and algorithms for checking the satisfiability of propositional LTL formulae can be integrated. This paves the way to employ efficient Satisfiability Modulo Theories solvers in the model-checking of infinite state systems. We illustrate our techniques on two examples.KeywordsModel CheckDecision ProcedureCombination MethodSafety PropertyReachability ProblemThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.