Star-free picture expressions are strictly weaker than first-order logic

  • Thomas Wilke
Session 7: Formal Languages II
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1256)


We exhibit a first-order definable picture language which we prove is not expressible by any star-free picture expression, i. e., it is not star-free. Thus first-order logic over pictures is strictly more powerful than star-free picture expressíons are. This is in sharp contrast with the situation with words: the well-known McNaughton-Papert theorem states that a word language is expressible by a first-order formula if and only if it is expressible by a star-free (word) expression.

The main ingredients of the non-expressibility result are a Fraïssé-style algebraic characterization of star freeness for picture languages and combinatorics on words.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Thomas Wilke
    • 1
  1. 1.Institut für Informatik und Praktische MathematikChristian-Albrechts-Universität zu KielKielGermany

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