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Efficiently Computing the Density of Regular Languages

  • Manuel Bodirsky
  • Tobias Gärtner
  • Timo von Oertzen
  • Jan Schwinghammer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2976)

Abstract

A regular language L is called dense if the fraction f m of words of length m over some fixed signature that are contained in L tends to one if m tends to infinity. We present an algorithm that computes the number of accumulation points of (f m ) in polynomial time, if the regular language L is given by a finite deterministic automaton, and can then also efficiently check whether L is dense. Deciding whether the least accumulation point of (f m ) is greater than a given rational number, however, is coNP-complete. If the regular language is given by a non-deterministic automaton, checking whether L is dense becomes PSPACE-hard. We will formulate these problems as convergence problems of partially observable Markov chains, and reduce them to combinatorial problems for periodic sequences of rational numbers.

Keywords

Markov Chain Rational Number Accumulation Point Regular Language Convergence Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Manuel Bodirsky
    • 1
  • Tobias Gärtner
    • 2
  • Timo von Oertzen
    • 2
  • Jan Schwinghammer
    • 3
  1. 1.Humboldt-Universität zu BerlinGermany
  2. 2.Universität des SaarlandesGermany
  3. 3.University of SussexUK

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