Provably Shorter Regular Expressions from Deterministic Finite Automata

(Extended Abstract)
  • Hermann Gruber
  • Markus Holzer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5257)

Abstract

We study the problem of finding good elimination orderings for the state elimination algorithm, which is one of the most popular algorithms for the conversion of finite automata into equivalent regular expressions. Based on graph separator techniques we are able to describe elimination strategies that remove states in large induced subgraphs that are “simple” like, e.g., independent sets or subgraphs of bounded treewidth, of the underlying automaton, that lead to regular expressions of moderate size. In particular, we show that there is an elimination ordering such that every language over a binary alphabet accepted by an n-state deterministic finite automaton has alphabetic width at most O(1.742n), which is, to our knowledge, the algorithm with currently the best known performance guarantee. Finally, we apply our technique to the question on the effect of language operations on regular expression size. In case of the intersection operation we prove an upper bound which matches, up to a small factor, a lower bound recently obtained in [9,10], and thus settles an open problem stated in [7].

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Hermann Gruber
    • 1
  • Markus Holzer
    • 2
  1. 1.Institut für InformatikLudwig-Maximilians-Universität MünchenMünchenGermany
  2. 2.Institut für InformatikTechnische Universität MünchenGarching bei MünchenGermany

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