Probabilistic and nondeterministic unary automata

  • We investigate unary regular languages and compare deterministic finite automata (DFA’s), nondeterministic finite automata (NFA’s) and probabilistic finite automata (PFA’s) with respect to their size. Given a unary PFA with n states and an e-isolated cutpoint, we show that the minimal equivalent DFA has at most n exp 1/2e states in its cycle. This result is almost optimal, since for any alpha < 1 a family of PFA’s can be constructed such that every equivalent DFA has at least n exp alpha/2e states. Thus we show that for the model of probabilistic automata with a constant error bound, there is only a polynomial blowup for cyclic languages. Given a unary NFA with n states, we show that efficiently approximating the size of a minimal equivalent NFA within the factor sqrt(n)/ln n is impossible unless P = NP. This result even holds under the promise that the accepted language is cyclic. On the other hand we show that we can approximate a minimal NFA within the factor ln n, if we are given a cyclic unary n-state DFA.

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Author:Gregor Gramlich
Editor:Branislav Rovan, Peter Vojtáš
Document Type:Article
Year of Completion:2003
Year of first Publication:2003
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2007/07/04
GND Keyword:Theoretische Informatik; Kongress; Preßburg <2003>; Online-Publikation
Page Number:8
Die Arbeit erhielt den "Best student paper award".
Überarbeitete Fassung von: Branislav Rovan ; Peter Vojtáš (Hrsg.): Mathematical foundations of computer science 2003 : 28th international symposium ; proceedings, Berlin ; Heidelberg ; New York ; Hong Kong ; London ; Milan ; Paris ; Tokyo : Springer, 2003, Lecture notes in computer science ; Vol. 2747, S. 460–469, ISBN: 978-3-540-40671-6, ISBN: 3-540-40671-9, ISBN: 978-3-540-45138-9, doi:10.1007/b11836
Source:Überarb. Fassung. - 1. Fassung in: Proceedings of Mathematical Foundations of Computer Science (MFCS), 2003. - Springer-Verlag. - Lecture Notes in Computer Science 2747, 2003, S. 460-469: Mathematical Foundations of Computer Science 28th International Sym
Institutes:Informatik und Mathematik / Informatik
Dewey Decimal Classification:0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 004 Datenverarbeitung; Informatik
Licence (German):License LogoDeutsches Urheberrecht