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### Ambiguity and Communication

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### Abstract

The ambiguity of a nondeterministic finite automaton (NFA) $N$ for input size $n$ is the maximal number of accepting computations of $N$ for an input of size $n$. For all $k,r \in \mathbb{N}$ we construct languages $L_{r,k}$ which can be recognized by NFA's with size $k \cdot$poly$(r)$ and ambiguity $O(n^k)$, but $L_{r,k}$ has only NFA's with exponential size, if ambiguity $o(n^k)$ is required. In particular, a hierarchy for polynomial ambiguity is obtained, solving a long standing open problem (Ravikumar and Ibarra, 1989, Leung, 1998).

### BibTeX - Entry

@InProceedings{hromkovic_et_al:LIPIcs:2009:1805,
author =	{Juraj Hromkovic and Georg Schnitger},
title =	{{Ambiguity and Communication}},
booktitle =	{26th International Symposium on Theoretical Aspects of Computer Science},
pages =	{553--564},
series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN =	{978-3-939897-09-5},
ISSN =	{1868-8969},
year =	{2009},
volume =	{3},
editor =	{Susanne Albers and Jean-Yves Marion},
publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address =	{Dagstuhl, Germany},
URL =		{http://drops.dagstuhl.de/opus/volltexte/2009/1805},
URN =		{urn:nbn:de:0030-drops-18054},
doi =		{http://dx.doi.org/10.4230/LIPIcs.STACS.2009.1805},
annote =	{Keywords: Nondeterministic finite automata, Ambiguity, Communication complexity}
}


 Keywords: Nondeterministic finite automata, Ambiguity, Communication complexity Seminar: 26th International Symposium on Theoretical Aspects of Computer Science Related Scholarly Article: Issue date: 2009 Date of publication: 2009

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