Computing All ℓ-Cover Automata Fast

  • Artur Jeż
  • Andreas Maletti
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6807)

Abstract

Given a language L and a number ℓ, an ℓ-cover automaton for L is a DFA M such that its language coincides with L on all words of length at most ℓ. It is known that an equivalent minimal ℓ-cover automaton can be constructed in time \(\mathcal{O}(n \log n)\), where n is the number of states of M. This is achieved by a clever and sophisticated variant of Hopcroft’s algorithm, which computes the ℓ-similarity inside the main algorithm. This contribution presents an alternative simple algorithm with running time \(\mathcal{O}(n \log n)\), in which the computation is split into three phases. First, a compact representation of the gap table is created. Second, this representation is enriched with information about the length of a shortest word leading to the states. These two steps are independent of the parameter ℓ. Third, the ℓ-similarity is extracted by simple comparisons against ℓ. In particular, this approach allows the calculation of all the sizes of minimal ℓ-cover automata (for all valid ℓ) in the same time bound.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Artur Jeż
    • 1
  • Andreas Maletti
    • 2
  1. 1.Institute of Computer ScienceUniversity of WrocławWrocławPoland
  2. 2.Institute for Natural Language ProcessingUniversität StuttgartStuttgartGermany

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