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.
Author: | Gregor Gramlich |
---|---|
URN: | urn:nbn:de:hebis:30-44876 |
DOI: | https://doi.org/10.1007/b11836 |
ISBN: | 978-3-540-45138-9 |
ISBN: | 978-3-540-40671-6 |
ISBN: | 3-540-40671-9 |
Editor: | Branislav Rovan, Peter Vojtáš |
Document Type: | Article |
Language: | English |
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 |
Note: | Die Arbeit erhielt den "Best student paper award". |
Note: | 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 |
HeBIS-PPN: | 188605797 |
Institutes: | Informatik und Mathematik / Informatik |
Dewey Decimal Classification: | 0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 004 Datenverarbeitung; Informatik |
Licence (German): | Deutsches Urheberrecht |