Efficient Analysis of Unambiguous Automata Using Matrix Semigroup Techniques

Authors Stefan Kiefer, Cas Widdershoven



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Author Details

Stefan Kiefer
  • University of Oxford, UK
Cas Widdershoven
  • University of Oxford, UK

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Stefan Kiefer and Cas Widdershoven. Efficient Analysis of Unambiguous Automata Using Matrix Semigroup Techniques. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 82:1-82:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.MFCS.2019.82

Abstract

We introduce a novel technique to analyse unambiguous Büchi automata quantitatively, and apply this to the model checking problem. It is based on linear-algebra arguments that originate from the analysis of matrix semigroups with constant spectral radius. This method can replace a combinatorial procedure that dominates the computational complexity of the existing procedure by Baier et al. We analyse the complexity in detail, showing that, in terms of the set Q of states of the automaton, the new algorithm runs in time O(|Q|^4), improving on an efficient implementation of the combinatorial algorithm by a factor of |Q|.

Subject Classification

ACM Subject Classification
  • Theory of computation → Automata over infinite objects
  • Theory of computation → Design and analysis of algorithms
Keywords
  • Algorithms
  • Automata
  • Markov Chains
  • Matrix Semigroups

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References

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