Mathematical systems theory

, Volume 24, Issue 1, pp 117–146 | Cite as

A geometrical view of the determinization and minimization of finite-state automata

  • Bruno Courcelle
  • Damian Niwinski
  • Andreas Podelski


With every finite-state word or tree automaton, we associate a binary relation on words or trees. We then consider the “rectangular decompositions” of this relation, i.e., the various ways to express it as a finite union of Cartesian products of sets of words or trees, respectively. We show that the determinization and the minimization of these automata correspond to simple geometrical reorganizations of the rectangular decompositions of the associated relations.


Computational Mathematic Binary Relation Finite Union Tree Automaton Geometrical View 
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Copyright information

© Springer-Verlag New York Inc. 1991

Authors and Affiliations

  • Bruno Courcelle
    • 1
  • Damian Niwinski
    • 2
  • Andreas Podelski
    • 3
  1. 1.Laboratoire d'InformatiqueUniversité Bordeaux-1Talence cedexFrance
  2. 2.Institute of MathematicsWarsaw University, PKiN IXWarszawaPoland
  3. 3.LITP, Université Paris-7Paris Cedex 05France

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