Characterizing co-NL by a group action

TL;DR

This paper explains Girard's novel approach using geometry of interaction in the hyperfinite factor to characterize the complexity class co-NL, providing detailed motivation, definitions, and a proof of the characterization.

Contribution

It offers a detailed explanation of Girard's method and proves that co-NL can be characterized through this innovative geometric approach.

Findings

Girard's geometry of interaction characterizes co-NL

Introduction of non-deterministic pointer machines as a computational model

Complete proof of co-NL characterization using this framework

Abstract

In a recent paper, Girard proposes to use his recent construction of a geometry of interaction in the hyperfinite factor in an innovative way to characterize complexity classes. We begin by giving a detailed explanation of both the choices and the motivations of Girard's definitions. We then provide a complete proof that the complexity class co-NL can be characterized using this new approach. We introduce as a technical tool the non-deterministic pointer machine, a concrete model to computes algorithms.