Reference:

Stefan Kiefer and Cas Widdershoven. Efficient analysis of unambiguous automata using matrix semigroup techniques. In Proceedings of the 44th International Symposium on Mathematical Foundations of Computer Science (MFCS), Leibniz International Proceedings in Informatics (LIPIcs), pages 82:1–82:13, 2019.

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|.

Suggested BibTeX entry:

@inproceedings{19KW-MFCS,
    author = {Stefan Kiefer and Cas Widdershoven},
    booktitle = {Proceedings of the 44th International Symposium on Mathematical Foundations of Computer Science (MFCS)},
    pages = {82:1--82:13},
    series = {Leibniz International Proceedings in Informatics (LIPIcs)},
    title = {Efficient Analysis of Unambiguous Automata Using Matrix Semigroup Techniques},
    year = {2019}
}