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Weak Minimization of DFA — An Algorithm and Applications

  • Bala Ravikumar
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2759)

Abstract

DFA minimization is a central problem in algorithm design and is based on the notion of DFA equivalence: Two DFA’s are equivalent if and only if they accept the same set of strings. In this paper, we propose a new notion of DFA equivalence (that we call weak-equivalence):We say that two DFA’s are weakly equivalent if they both accept the same number of strings of length k for every k. The motivation for this problem is as follows. A large number of counting problems can be solved by encoding the combinatorial objects we want to count as strings over a finite alphabet. If the collection of encoded strings is accepted by a DFA, then standard algorithms from computational linear algebra can be used to solve the counting problem efficiently. When applying this approach to largwe-scale applications, the bottleneck is the space complexity since the computation involves a matrix of order k × k if k is the size of the underlying DFA M. This leads to the natural question: Is there a smaller DFA that is weakly equivalent to M? We present an algorithm of time complexity O(k 2) to find a compact DFA equivalent to a given DFA. We illustrate, in the case of tiling problem, that our algorithm reduces a (strongly minimal) DFA by a factor close to 2.

Keywords

Transfer Matrix Simple Path Input Symbol Grid Graph Counting 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 2003

Authors and Affiliations

  • Bala Ravikumar
    • 1
  1. 1.Department of Computer ScienceSonoma State UniversityRohnert Park

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