Top

Published in:

2018 | OriginalPaper | Chapter

On Emptiness and Membership Problems for Set Automata

Authors : A. Rubtsov, M. Vyalyi

Published in: Computer Science – Theory and Applications

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

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 Kutrib et al. in 2014 in [2, 3].

In this paper we characterize algorithmic complexity of the emptiness and membership problems for set automata. More definitely, we prove that both problems are \({\mathbf {PSPACE}}\)-complete for both kinds of set automata.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

previous chapter On the Decision Trees with Symmetries

next chapter On Strong NP-Completeness of Rational Problems

The structural Propositions 8 and 9 hold for all query languages. Lemma 10 and the \({\mathbf {PSPACE}}\) algorithm below are applied to regular query languages only.

Kozen, D.: Lower bounds for natural proof systems. In: Proceedings of the 18th Annual Symposium on Foundations of Computer Science, SFCS 1977, pp. 254–266. IEEE Computer Society, Washington, D.C. (1977)

Kutrib, M., Malcher, A., Wendlandt, M.: Deterministic set automata. In: Shur, A.M., Volkov, M.V. (eds.) DLT 2014. LNCS, vol. 8633, pp. 303–314. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09698-8_27CrossRef

Kutrib, M., Malcher, A., Wendlandt, M.: Regularity and size of set automata. In: Jürgensen, H., Karhumäki, J., Okhotin, A. (eds.) DCFS 2014. LNCS, vol. 8614, pp. 282–293. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09704-6_25CrossRefMATH

Kutrib, M., Malcher, A., Wendlandt, M.: Set automata. Int. J. Found. Comput. Sci. 27(02), 187–214 (2016)MathSciNetCrossRefMATH

Lange, K.-J., Rossmanith, P.: The emptiness problem for intersections of regular languages. In: Havel, I.M., Koubek, V. (eds.) MFCS 1992. LNCS, vol. 629, pp. 346–354. Springer, Heidelberg (1992). https://doi.org/10.1007/3-540-55808-X_33CrossRef

Lange, K.-J., Reinhardt, K.: Set automata. In: Bridges, D.S., Calude, C., Gibbons, J., Reeves, S., Witten, L. (eds.) Combinatorics, Complexity, Logic. Proceedings of the DMTCS 1996, pp. 321–329. Springer, Heidelberg (1996)

Rubtsov, A.A., Vyalyi, M.N.: On computational complexity of set automata. In: Charlier, É., Leroy, J., Rigo, M. (eds.) DLT 2017. LNCS, vol. 10396, pp. 332–344. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-62809-7_25CrossRef

Title: On Emptiness and Membership Problems for Set Automata
Authors: A. Rubtsov
M. Vyalyi
Publisher: Springer International Publishing
Book: Computer Science – Theory and Applications
Print ISBN: 978-3-319-90529-7

Electronic ISBN: 978-3-319-90530-3

Copyright Year: 2018
DOI: https://doi.org/10.1007/978-3-319-90530-3_25

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"

Premium Partner