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Reducing Acceptance Marks in Emerson-Lei Automata by QBF Solving

Authors Tereza Schwarzová , Jan Strejček , Juraj Major



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Author Details

Tereza Schwarzová
  • Masaryk University, Brno, Czech Republic
Jan Strejček
  • Masaryk University, Brno, Czech Republic
Juraj Major
  • Masaryk University, Brno, Czech Republic

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Tereza Schwarzová, Jan Strejček, and Juraj Major. Reducing Acceptance Marks in Emerson-Lei Automata by QBF Solving. In 26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 271, pp. 23:1-23:20, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.SAT.2023.23

Abstract

This paper presents a novel application of QBF solving to automata reduction. We focus on Transition-based Emerson-Lei automata (TELA), which is a popular formalism that generalizes many traditional kinds of automata over infinite words including Büchi, co-Büchi, Rabin, Streett, and parity automata. Transitions in a TELA are labelled with acceptance marks and its accepting formula is a positive Boolean combination of atoms saying that a particular mark has to be visited infinitely or finitely often. Algorithms processing these automata are often very sensitive to the number of acceptance marks. We introduce a new technique for reducing the number of acceptance marks in TELA based on satisfiability of quantified Boolean formulas (QBF). We evaluated our reduction technique on TELA produced by state-of-the-art tools of the libraries Owl and Spot and by the tool ltl3tela. The technique reduced some acceptance marks in automata produced by all the tools. On automata with more than one acceptance mark obtained by translation of LTL formulas from literature with tools Delag and Rabinizer 4, our technique reduced 27.7% and 39.3% of acceptance marks, respectively. The reduction was even higher on automata from random formulas.

Subject Classification

ACM Subject Classification
  • Theory of computation → Logic
  • Theory of computation → Automata over infinite objects
Keywords
  • Emerson-Lei automata
  • TELA
  • automata reduction
  • QBF
  • telatko

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References

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