Logical definability of NP-optimisation problems with monadic auxiliary predicates

  • Clemens Lautemann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 702)

Abstract

Given a first-order formula ϕ with predicate symbols e1...el, so,...,sr, an NP-optimisation problem on <e1,...,el>-structures can be defined as follows: for every <e1,...,el>-structure G, a sequence <S0,...,Sr> of relations on G is a feasible solution iff <G, S0,....Sr> satisfies ϕ, and the value of such a solution is defined to be ¦S0¦. In a strong sense, every polynomially bounded NP-optimisation problem has such a representation, however, it is shown here that this is no longer true if the predicates s1, ...,sr are restricted to be monadic. The result is proved by an Ehrenfeucht-Fraïssé game and remains true in several more general situations.

Keywords

Chromatic Number Predicate Symbol Winning Strategy Clique Number Chromatic Index 
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 1993

Authors and Affiliations

  • Clemens Lautemann
    • 1
  1. 1.Institut für InformatikJohannes Gutenberg-Universität MainzDeutschland

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