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computational complexity

, Volume 25, Issue 4, pp 775–814 | Cite as

The complexity of intersecting finite automata having few final states

  • Michael Blondin
  • Andreas Krebs
  • Pierre McKenzie
Article

Abstract

The problem of determining whether several finite automata accept a word in common is closely related to the well-studied membership problem in transformation monoids. We raise the issue of limiting the number of final states in the automata intersection problem. For automata with two final states, we show the problem to be \({\oplus}\)L-complete or NP-complete according to whether a nontrivial monoid other than a direct product of cyclic groups of order 2 is allowed in the automata. We further consider idempotent commutative automata and (Abelian, mainly) group automata with one, two, or three final states over a singleton or larger alphabet, elucidating (under the usual hypotheses on complexity classes) the complexity of the intersection nonemptiness and related problems in each case.

Keywords

Finite automata intersection problem monoids logspace NP-complete point-spread problem 

Subject classification

68Q15 68Q25 68Q17 03D15 68Q70 

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Copyright information

© Springer Basel 2014

Authors and Affiliations

  • Michael Blondin
    • 1
    • 2
  • Andreas Krebs
    • 3
  • Pierre McKenzie
    • 1
    • 2
  1. 1.Département d’informatique et de recherche opérationnelleUniversité de MontréalMontrealCanada
  2. 2.Laboratoire Spécification et VérificationENS CachanCachanFrance
  3. 3.Wilhelm-Schickard-Institut für InformatikUniversität TübingenTübingenGermany

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