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The logic of explicitly presentation-invariant circuits

  • Martin Otto
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1258)

Abstract

We give a novel and simple characterization of first-order logic and its infinitary variants with bounded numbers of variables in terms of circuit computation. The main feature of the proposed circuit model of explicitly symmetric circuits is, that genericity in computations over structures is guaranteed through full combinatorial symmetry of circuits with respect to permutations of the input representation.

Definability in the bounded variable fragment of infinitary logic is equivalent with recognizability in such explicitly symmetric circuits in which the orbits of nodes under symmetry operations are polynomially bounded. First-order definability is equivalent with recognizability in finite depth circuits of that kind.

Keywords

Circuit complexity generic computation finite model theory 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Martin Otto
    • 1
  1. 1.Mathematische Grundlagen der InformatikRWTH AachenAachenGermany

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