The tractability frontier for NFA minimization

  • Authors:

  • Henrik Björklund;Wim Martens

  • Affiliations:

  • Department of Computing Science, Umeå University, 90187 Umeå, Sweden;Lehrstuhl Informatik I, Technical University of Dortmund, 44221 Dortmund, Germany

  • Venue:
  • Journal of Computer and System Sciences
  • Year:
  • 2012

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Abstract

We prove that minimizing finite automata is NP-hard for almost all classes of automata that extend the class of deterministic finite automata. More specifically, we show that minimization is NP-hard for all finite automata classes that subsume the class of @dNFAs which accept strings of length at most three. Here, @dNFAs are the finite automata that are unambiguous, allow at most one state q with a non-deterministic transition for at most one alphabet symbol a, and are allowed to visit state q at most once in a run. As a corollary, we also obtain that the same result holds for all finite automata classes that subsume that class of finite automata that are unambiguous, have at most two initial states, and accept strings of length at most two.