Logic Programming and Logarithmic Space

TL;DR

This paper introduces an algebraic framework linking logic programming to logspace computation, demonstrating that word acceptance can be decided within logarithmic space and relating observations to two-way multi-head finite automata.

Contribution

It provides a novel algebraic and proof-theoretic characterization of logspace computation using logic programming and geometry of interaction.

Findings

Word acceptance reduces to graph acyclicity within log space.

Observations are as expressive as two-way multi-head finite automata.

The approach offers a new proof-theoretic perspective on logspace complexity.

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 synctactic 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 multi-heads finite automata, a kind of pointer machines that is a standard model of logarithmic space computation.