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.

线性时序逻辑（\(\textsf{LTL}\,\)）及其在有限迹上解释的变体（\(\textsf{LTL}_{\textsf{f}\,}\)）是最流行的规范之一形式验证、人工智能等领域的语言。在本文中，我们重点关注\(\textsf{LTL}\,\)和\(\textsf{LTL}_{\textsf{f}\,}\)公式的可满足性问题，为此许多技术已经被采用是在过去几十年里设计出来的。其中包括画面系统，其中最新的是雷诺兹的树形画面。我们提供了一种基于 SAT 的算法，用于基于 Reynolds 表格的\(\textsf{LTL}\,\)和\(\textsf{LTL}_{\textsf{f}\,}\)可满足性检查，并证明了其正确性并讨论通过在 BLACK 可满足性检查器中实现而获得的实验结果。