SAT Meets Tableaux for Linear Temporal Logic Satisfiability

Luca Geatti, Nicola Gigante, Angelo Montanari, Gabriele Venturato

Abstract: Linear temporal logic (\(\textsf{LTL}\,\)) and its variant interpreted on finite traces (\(\textsf{LTL}_{\textsf{f}\,}\)) 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 \(\textsf{LTL}\,\)and \(\textsf{LTL}_{\textsf{f}\,}\)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 \(\textsf{LTL}\,\)and \(\textsf{LTL}_{\textsf{f}\,}\)satisfiability checking based on Reynolds’ tableau, proving its correctness and discussing experimental results obtained through its implementation in the BLACK satisfiability checker.