Direct translation of LTL formulas to Büchi automata

TLDR: An improved tableau-based algorithm is proposed, which generates transition-based Büchi automata for given LTL formulas directly, by applying an efficient on-the-fly degeneralization.

Abstract: The translation from LTL formulas to Buchi automata plays a key role in explicit model checking. Most algorithms for obtaining Buchi automata from LTL formulas involve intermediate forms, and perform simplifications on the intermediate or the final translation product. In this paper an improved tableau-based algorithm is proposed, which generates transition-based Buchi automata for given LTL formulas directly, by applying an efficient on-the-fly degeneralization. The algorithm circumvents the intermediate steps and the simplification process that follows, and therefore performs more efficiently. On-the-fly simplifications as well as BDD presentations are adopted in the algorithm to gain significant reduction both on the size of result automata and on the computational complexity. With some experimental results, a comparison between our method and previous work is given. It is shown that our approach yields smaller automata for the formulas commonly found in the literature, especially for those containing a large portion of GU- or GF-formulas.