SAT Meets Tableaux for Linear Temporal Logic Satisfiability

Abstract

AbstractLinear temporal logic ($$\textsf{LTL}\,$$ LTL ) and its variant interpreted on finite traces ($$\textsf{LTL}_{\textsf{f}\,}$$ LTL f ) are among the most popular specification languages in the fields of formal verification, artificial intelligence, and others. In this paper, we focus on the satisfiability problem for $$\textsf{LTL}\,$$ LTL and $$\textsf{LTL}_{\textsf{f}\,}$$ LTL f formulas, for which many techniques have been devised during the last decades. Among these are tableau systems, of which the most recent is Reynolds’ tree-shaped tableau. We provide a SAT-based algorithm for $$\textsf{LTL}\,$$ LTL and $$\textsf{LTL}_{\textsf{f}\,}$$ LTL f satisfiability checking based on Reynolds’ tableau, proving its correctness and discussing experimental results obtained through its implementation in the BLACK satisfiability checker.