Expansions of pseudofinite structures and circuit and proof complexity

TL;DR

This paper explores how expanding pseudofinite structures can impact computational complexity, particularly suggesting that certain expansions could imply NP is not closed under complement if one-way permutations exist.

Contribution

It introduces a model-theoretic approach to constructing expansions of pseudofinite structures and connects these to major open problems in computational complexity.

Findings

A specific expansion could imply NP is not closed under complement

Framework links model theory with circuit and proof complexity

Provides examples relevant to computational complexity

Abstract

I shall describe a general model-theoretic task to construct expansions of pseudofinite structures and discuss several examples of particular relevance to computational complexity. Then I will present one specific situation where finding a suitable expansion would imply that, assuming a one-way permutation exists, the computational class NP is not closed under complementation.