NP on Logarithmic Space

Unification and Logarithmic Space

We present an algebraic characterization of the complexity classes Logspace and NLogspace, using an algebra with a composition law based on unification. This new bridge between unification and complexity classes is inspired from proof theory and more specifically linear logic and Geometry of Interaction. We show how unification can be used to build a model of computation by means of specific su...

Logarithmic Space and Permutations

In a recent work, Girard [1] proposed a new and innovative approach to computational complexity based on the proofs-as-programs correspondence. In a previous paper [2], the authors showed how Girard proposal succeeds in obtaining a new characterization of co-NL languages as a set of operators acting on a Hilbert Space. In this paper, we extend this work by showing that it is also possible to de...

Unambiguous Functions in Logarithmic Space

We investigate different variants of unambiguity in the context of computing multi-valued functions. We propose a modification to the standard computation models of Turing machines and configuration graphs, which allows for unambiguity-preserving composition. We define a notion of reductions (based on function composition), which allows nondeterminism but controls its level of ambiguity. In lig...

Unambiguous Logarithmic Space Bounded Computations

Logic Programming and Logarithmic Space

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 observatio...