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An nlogn Algorithm for Hyper-minimizing States in a (Minimized) Deterministic Automaton

  • Markus Holzer
  • Andreas Maletti
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5642)

Abstract

We improve a recent result [A. Badr: Hyper-Minimization in O(n 2). In Proc. CIAA, LNCS 5148, 2008] for hyper-minimized finite automata. Namely, we present an O(nlogn) algorithm that computes for a given finite deterministic automaton (dfa) an almost equivalent dfa that is as small as possible—such an automaton is called hyper-minimal. Here two finite automata are almost equivalent if and only if the symmetric difference of their languages is finite. In other words, two almost-equivalent automata disagree on acceptance on finitely many inputs. In this way, we solve an open problem stated in [A. Badr, V. Geffert, I. Shipman: Hyper-minimizing minimized deterministic finite state automata. RAIRO Theor. Inf. Appl. 43(1), 2009] and by Badr. Moreover, we show that minimization linearly reduces to hyper-minimization, which shows that the time-bound O(n logn) is optimal for hyper-minimization.

Keywords

Regular Language Finite Automaton Input Symbol State Automaton Lossless Compression 
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 2009

Authors and Affiliations

  • Markus Holzer
    • 1
  • Andreas Maletti
    • 2
  1. 1.Institut für InformatikUniversität GiessenGiessenGermany
  2. 2.Departament de Filologies RomàniquesUniversitat Rovira i VirgiliTarragonaSpain

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