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Logical definability of NP-optimisation problems with monadic auxiliary predicates

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Computer Science Logic (CSL 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 702))

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Abstract

Given a first-order formula ϕ with predicate symbols e 1...e l, s o,...,sr, an NP-optimisation problem on <e 1,...,el>-structures can be defined as follows: for every <e 1,...,el>-structure G, a sequence <S 0,...,Sr> of relations on G is a feasible solution iff <G, S 0,....S r> satisfies ϕ, and the value of such a solution is defined to be ¦S 0¦. 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 s 1, ...,s r are restricted to be monadic. The result is proved by an Ehrenfeucht-Fraïssé game and remains true in several more general situations.

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Authors and Affiliations

  1. Institut für Informatik, Johannes Gutenberg-Universität Mainz, Deutschland

    Clemens Lautemann

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  1. Clemens Lautemann
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Editor information

E. Börger G. Jäger H. Kleine Büning S. Martini M. M. Richter

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© 1993 Springer-Verlag Berlin Heidelberg

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Lautemann, C. (1993). Logical definability of NP-optimisation problems with monadic auxiliary predicates. In: Börger, E., Jäger, G., Kleine Büning, H., Martini, S., Richter, M.M. (eds) Computer Science Logic. CSL 1992. Lecture Notes in Computer Science, vol 702. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56992-8_19

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  • DOI: https://doi.org/10.1007/3-540-56992-8_19

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  • Print ISBN: 978-3-540-56992-3

  • Online ISBN: 978-3-540-47890-4

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