The Tractability Frontier for NFA Minimization

  • Henrik Björklund
  • Wim Martens
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5126)


We essentially show that minimizing finite automata is NP-hard as soon as one deviates from the class of deterministic finite automata. More specifically, we show that minimization is NP-hard for all finite automata classes that subsume the class that is unambiguous, allows at most one state q with a non-deterministic transition for at most one alphabet symbol a, and is allowed to visit state q at most once in a run. Furthermore, this result holds even for automata that only accept finite languages.


Minimization Problem Regular Expression Vertex Cover Regular Language Deterministic Finite Automaton 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Henrik Björklund
    • 1
  • Wim Martens
    • 1
  1. 1.TU Dortmund 

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