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One quantifier will do in existential monadic second-order logic over pictures

  • Oliver Matz
Contributed Papers Picture Languages - Function Systems/Complexity
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1450)

Abstract

We show that every formula of the existential fragment of monadic second-order logic over picture models (i.e., finite, two-dimensional, coloured grids) is equivalent to one with only one existential monadic quantifier.

The corresponding claim is true for the class of word models ([Tho82]) but not for the class of graphs ([Ott95]).

The class of picture models is of particular interest because it has been used to show the strictness of the different (and more popular) hierarchy of quantifier alternation.

Keywords

Existential Quantifier Fixed Height Boundary Symbol Word Model Quantifier Alternation 
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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References

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Oliver Matz
    • 1
  1. 1.Institut für Informatik und Praktische MathematikChristian-Albrechts-Universität KielKielGermany

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