Constraint LTL satisfiability checking without automata

Abstract This paper introduces a novel technique to decide the satisfiability of formulae written in the language of Linear Temporal Logic with both future and past operators and atomic formulae belonging to constraint system D (CLTLB( D ) for short). The technique is based on the concept of bounded satisfiability, and hinges on an encoding of CLTLB( D ) formulae into QF-EU D , the theory of quantifier-free equality and uninterpreted functions combined with D . Similarly to standard LTL, where bounded model-checking and SAT-solvers can be used as an alternative to automata-theoretic approaches to model-checking, our approach allows users to solve the satisfiability problem for CLTLB( D ) formulae through SMT-solving techniques, rather than by checking the emptiness of the language of a suitable automaton. The technique is effective, and it has been implemented in our Z ot formal verification tool.

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