Abstract
A self-verifying finite automaton (SVFA) is a nondeterministic automaton whose computation can accept, reject, or give no answer. Every word is guaranteed to be either accepted or rejected, and the automaton can not give contradictory answers. This paper examines the computational complexity of several decision problems for SVFAs. First, determining whether a given automaton is an SVFA is PSPACE-complete. All other problems are therefore stated as promise problems. The complexity of (non-)emptiness, universality, and equivalence is comparable to that for deterministic automata. On the other hand, SVFA membership and minimization problems, as well as several counting problems, behave more like their nondeterministic variants.
J. Jirásek Jr.—Supported, in part, by Natural Sciences and Engineering Research Council of Canada Grant (Ian McQuillan, 2016-06172).
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Àlvarez, C., Jenner, B.: A very hard log-space counting class. Theor. Comput. Sci. 107(1), 3–30 (1993)
Cho, S., Huynh, D.T.: The parallel complexity of finite-state automata problems. Inform. Comput. 97, 1–22 (1992)
Ďuriš, P., Hromkovič, J., Rolim, J.D.P., Schnitger, G.: Las Vegas versus determinism for one-way communication complexity, finite automata, and polynomial-time computations. In: Reischuk, R., Morvan, M. (eds.) STACS 1997. LNCS, vol. 1200, pp. 117–128. Springer, Heidelberg (1997). https://doi.org/10.1007/BFb0023453
Holzer, M., Kutrib, M.: Descriptional and computational complexity of finite automata—a survey. Inform. Comput. 209(3), 456–470 (2011)
Immerman, N.: Nondeterministic space is closed under complementation. SIAM J. Comput. 17(5), 935–938 (1988)
Jiang, T., Ravikumar, B.: Minimal NFA problems are hard. SIAM J. Comput. 22(6), 1117–1141 (1993)
Jirásek, J.Š., Jirásková, G., Szabari, A.: Operations on self-verifying finite automata. In: Beklemishev, L.D., Musatov, D.V. (eds.) CSR 2015. LNCS, vol. 9139, pp. 231–261. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20297-6_16
Jirásková, G., Pighizzini, G.: Optimal simulation of self-verifying automata by deterministic automata. Inform. Comput. 209(3), 528–535 (2011)
Jones, N.: Space-bounded reducibility among combinatorial problems. J. Comput. Syst. Sci. 11, 68–85 (1975)
Meyer, A.R., Stockmeyer, L.J.: The equivalence problem for regular expressions with squaring requires exponential time. In: Proceedings of the 13th Annual Symposium on Switching and Automata Theory, pp. 125–129. IEEE Society Press (1972)
Szelepcsényi, R.: The method of forced enumeration for nondeterministic automata. Acta Inform. 26(3), 279–284 (1988)
Valiant, L.G.: The complexity of computing the permanent. Theor. Comput. Sci. 8(2), 189–201 (1979)
Valiant, L.G.: The complexity of enumeration and reliability problems. SIAM J. Comput. 8(3), 410–421 (1979)
Acknowledgements
We would like to thank Galina Jirásková for her input and for generously proofreading the paper.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this paper
Cite this paper
Holzer, M., Jakobi, S., Jirásek, J. (2018). Computational Complexity of Decision Problems on Self-verifying Finite Automata. In: Hoshi, M., Seki, S. (eds) Developments in Language Theory. DLT 2018. Lecture Notes in Computer Science(), vol 11088. Springer, Cham. https://doi.org/10.1007/978-3-319-98654-8_33
Download citation
DOI: https://doi.org/10.1007/978-3-319-98654-8_33
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-98653-1
Online ISBN: 978-3-319-98654-8
eBook Packages: Computer ScienceComputer Science (R0)