SOFSEM 2006: Theory and Practice of Computer Science
Volume 3831 of the series Lecture Notes in Computer Science pp 379-388
On Separating Constant from Polynomial Ambiguity of Finite Automata
- Joachim KupkeAffiliated withETH Zurich
Abstract
The degree of nondeterminism of a finite automaton can be measured by means of its ambiguity function. In many instances, whenever automata are allowed to be (substantially) less ambiguous, it is known that the number of states needed to recognize at least some languages increases exponentially. However, when comparing constantly ambiguous automata with polynomially ambiguous ones, the question whether there are languages such that the inferior class of automata requires exponentially many states more than the superior class to recognize them is still an open problem. The purpose of this paper is to suggest a family of languages that seems apt for a proof of this (conjectured) gap. As a byproduct, we derive a new variant of the proof of the existence of a superpolynomial gap between polynomial and fixed-constant ambiguity. Although our candidate languages are defined over a huge alphabet, we show how to overcome this drawback.
- Title
- On Separating Constant from Polynomial Ambiguity of Finite Automata
- Book Title
- SOFSEM 2006: Theory and Practice of Computer Science
- Book Subtitle
- 32nd Conference on Current Trends in Theory and Practice of Computer Science, Merin, Czech Republic, January 21-27, 2006. Proceedings
- Pages
- pp 379-388
- Copyright
- 2006
- DOI
- 10.1007/11611257_36
- Print ISBN
- 978-3-540-31198-0
- Online ISBN
- 978-3-540-32217-7
- Series Title
- Lecture Notes in Computer Science
- Series Volume
- 3831
- Series ISSN
- 0302-9743
- Publisher
- Springer Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
- Additional Links
- Topics
- Industry Sectors
- eBook Packages
- Editors
-
- Jiří Wiedermann (16)
- Gerard Tel (17)
- Jaroslav Pokorný (18)
- Mária Bieliková (19)
- Július Štuller (16)
- Editor Affiliations
-
- 16. Institute of Computer Science, Academy of Sciences of the Czech Republic
- 17. Department of Information and Computer Sciences, University of Utrecht
- 18. Faculty of Mathematics and Physics, Charles University
- 19. Institute of Informatics and Software Engineering Faculty of Informatics and Information technologies, Slovak University of Technology
- Authors
-
- Joachim Kupke (20)
- Author Affiliations
-
- 20. ETH Zurich, Zurich, Switzerland
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