Abstract
We consider a computational model which is known as set automata. The set automata are one-way finite automata with an additional storage—the set. There are two kinds of set automata—the deterministic and the nondeterministic ones. We denote them as DSA and NSA respectively. The model was introduced by M. Kutrib, A. Malcher, M. Wendlandt in 2014 in [3, 4]. It was shown that DSA-languages look similar to DCFL due to their closure properties and NSA-languages look similar to CFL due to their undecidability properties.
In this paper we show that this similarity is natural: we prove that languages recognizable by NSA form a rational cone, so as CFL. The main topic of this paper is computational complexity: we prove that languages recognizable by DSA belong to \({\mathbf {P}}\), and the word membership problem is \({\mathbf {P}}\)-complete for DSA without \(\varepsilon \)-loops; languages recognizable by NSA are in \({\mathbf {NP}}\), and there are \({\mathbf {NP}}\)-complete languages among them. Also we prove that the emptiness problem is \({\mathbf {PSPACE}}\)-hard for DSA.
Supported in part by RFBR grant 17–01–00300. The study has been funded by the Russian Academic Excellence Project ‘5–100’.
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Acknowledgements
We thank Dmitry Chistikov for the feedback and discussion of the text’s results and suggestion for improvements and anonymous referees for helpful comments.
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Rubtsov, A.A., Vyalyi, M.N. (2017). On Computational Complexity of Set Automata. In: Charlier, É., Leroy, J., Rigo, M. (eds) Developments in Language Theory. DLT 2017. Lecture Notes in Computer Science(), vol 10396. Springer, Cham. https://doi.org/10.1007/978-3-319-62809-7_25
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DOI: https://doi.org/10.1007/978-3-319-62809-7_25
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