Separating exponentially ambiguous NFA from polynomially ambiguous NFA

Leung, Hing

doi:10.1007/3-540-57568-5_252

Separating exponentially ambiguous NFA from polynomially ambiguous NFA

Hing Leung¹

Conference paper
First Online: 01 January 2005

168 Accesses
3 Citations

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 762))

Abstract

We resolve an open problem raised by Ravikumar and Ibarra on the succinctness of representations relating to the types of ambiguity of finite automata. We show that there exists a family of nondeterministic finite automata {A _n} over a two-letters alphabet such that, for any positive integer n, A _n is exponentially ambiguous and has n states, whereas the smallest equivalent deterministic finite automaton has 2ⁿ states and any smallest equivalent polynomially ambiguous finite automaton has 2ⁿ− 1 states.

This research is supported by an Alexander von Humboldt research fellowship. It was done while the author was visiting the Univerisity of Frankfurt, Germany.

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Authors and Affiliations

Department of Computer Science, New Mexico State University, 88003, Las Cruces, NM, USA
Hing Leung

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Hing Leung
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K. W. Ng P. Raghavan N. V. Balasubramanian F. Y. L. Chin

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Leung, H. (1993). Separating exponentially ambiguous NFA from polynomially ambiguous NFA. In: Ng, K.W., Raghavan, P., Balasubramanian, N.V., Chin, F.Y.L. (eds) Algorithms and Computation. ISAAC 1993. Lecture Notes in Computer Science, vol 762. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57568-5_252

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DOI: https://doi.org/10.1007/3-540-57568-5_252
Published: 01 June 2005
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-57568-9
Online ISBN: 978-3-540-48233-8
eBook Packages: Springer Book Archive

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