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Antichain with SAT and Tries

Authors Lukáš Holík , Pavol Vargovčík

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Author Details

Lukáš Holík
  • Faculty of Information Technology, Brno University of Technology, Czech Republic
Pavol Vargovčík
  • Faculty of Information Technology, Brno University of Technology, Czech Republic

Funding

This work was supported by the Czech Ministry of Education, Youth and Sports ERC.CZ project LL1908 and the FIT BUT internal project FIT-S-23-8151.

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Lukáš Holík and Pavol Vargovčík. Antichain with SAT and Tries. In 27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 305, pp. 15:1-15:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.SAT.2024.15

Abstract

We introduce a SAT-enabled version of an antichain algorithm for checking language emptiness of alternating finite automata (AFA) with complex transition relations encoded as compact logical formulae. The SAT solver is used to compute predecessors of AFA configurations, and at the same time, to evaluate the subsumption of newly found configurations in the antichain of the previously found ones. The algorithm could be naively implemented by an incremental SAT solver where the growing antichain is represented by adding new clauses. To make it efficient, we 1) force the SAT solver to prioritize largest/subsumption-strongest predecessors (so that weaker configurations are not even generated), and 2) store the antichain clauses in a special variant of a trie that allows fast subsumption testing. The experimental results suggest that the resulting emptiness checker is very efficient compared to the state of the art and that our techniques improve the performance of the SAT solver.

Subject Classification

ACM Subject Classification
  • Theory of computation → Logic and verification
  • Theory of computation → Regular languages
Keywords
  • SAT
  • Trie
  • Antichain
  • Alternating automata
  • Subset query

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