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URN: urn:nbn:de:0030-drops-33474
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A Tight Lower Bound for Streett Complementation

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Abstract

Finite automata on infinite words (omega-automata) proved to be a powerful weapon for modeling and reasoning infinite behaviors of reactive systems. Complementation of omega-automata is crucial in many of these applications. But the problem is non-trivial; even after extensive study during the past two decades, we still have an important type of omega-automata, namely Streett automata, for which the gap between the current best lower bound 2^(Omega(n lg nk)) and upper bound 2^(O (nk lg nk)) is substantial, for the Streett index size k can be exponential in the number of states n. In a previous work we showed a construction for complementing Streett automata with the upper bound 2^(O(n lg n+nk lg k)) for k = O(n) and 2^(O(n^2 lg n)) for k = omega(n). In this paper we establish a matching lower bound 2^(Omega (n lg n+nk lg k)) for k = O(n) and 2^(Omega (n^2 lg n)) for k = omega(n), and therefore showing that the construction is asymptotically optimal with respect to the ^(Theta(.)) notation.

BibTeX - Entry

@InProceedings{cai_et_al:LIPIcs:2011:3347,
  author =	{Yang Cai and Ting Zhang},
  title =	{{A Tight Lower Bound for Streett Complementation}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011)},
  pages =	{339--350},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-34-7},
  ISSN =	{1868-8969},
  year =	{2011},
  volume =	{13},
  editor =	{Supratik Chakraborty and Amit Kumar},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2011/3347},
  URN =		{urn:nbn:de:0030-drops-33474},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.FSTTCS.2011.339},
  annote =	{Keywords: omega-automata, Streett automata, complementation, lower bounds}
}

Keywords: omega-automata, Streett automata, complementation, lower bounds
Seminar: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011)
Issue date: 2011
Date of publication: 2011


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