Interaction Graphs: Nondeterministic Automata

TL;DR

This paper explores semantic characterisations of sublinear nondeterministic complexity classes using logic-based and geometric approaches, linking implicit computational complexity with group actions and measure-preserving maps.

Contribution

It introduces new semantic characterisations of sublinear nondeterministic classes based on geometric group actions within the framework of implicit computational complexity.

Findings

Semantic characterisations of sublinear nondeterministic classes

Connection between ICC and geometric group actions

Framework based on measure-preserving maps

Abstract

This paper exhibits a series of semantic characterisations of sublinear nondeterministic complexity classes. These results fall into the general domain of logic-based approaches to complexity theory and so-called implicit computational complexity (ICC), i.e. descriptions of complexity classes without reference to specific machine models. In particular, it relates strongly to ICC results based on linear logic since the semantic framework considered stems from work on the latter. Moreover, the obtained characterisations are of a geometric nature: each class is characterised by a specific action of a group by measure-preserving maps.