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Logic Programming and Logarithmic Space

  • Clément Aubert
  • Marc Bagnol
  • Paolo Pistone
  • Thomas Seiller
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8858)

Abstract

We present an algebraic view on logic programming, related to proof theory and more specifically linear logic and geometry of interaction. Within this construction, a characterization of logspace (deterministic and non-deterministic) computation is given via a syntactic restriction, using an encoding of words that derives from proof theory.

We show that the acceptance of a word by an observation (the counterpart of a program in the encoding) can be decided within logarithmic space, by reducing this problem to the acyclicity of a graph. We show moreover that observations are as expressive as two-ways multihead finite automata, a kind of pointer machine that is a standard model of logarithmic space computation.

Keywords

Implicit Complexity Unification Logic Programming Logarithmic Space Proof Theory Pointer Machines Geometry of Interaction Automata 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Clément Aubert
    • 1
  • Marc Bagnol
    • 1
  • Paolo Pistone
    • 1
  • Thomas Seiller
    • 2
  1. 1.CNRS, Centrale Marseille, I2M UMR 7373Aix Marseille UniversitéMarseilleFrance
  2. 2.I.H.É.S., Le Bois-MarieBures-sur-YvetteFrance

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