Sublogarithmic uniform Boolean proof nets

TL;DR

This paper introduces a new AC0 translation for uniform Boolean proof nets, enabling the encoding of constant-depth circuits and comparison of complexity classes below logspace, advancing the understanding of parallel computation models.

Contribution

It presents a novel AC0 translation for uniform Boolean proof nets, simplifying the comparison of complexity classes below logspace.

Findings

Enables encoding of constant-depth circuits

Allows comparison of classes below logspace

Simplifies translation between models

Abstract

Using a proofs-as-programs correspondence, Terui was able to compare two models of parallel computation: Boolean circuits and proof nets for multiplicative linear logic. Mogbil et. al. gave a logspace translation allowing us to compare their computational power as uniform complexity classes. This paper presents a novel translation in AC0 and focuses on a simpler restricted notion of uniform Boolean proof nets. We can then encode constant-depth circuits and compare complexity classes below logspace, which were out of reach with the previous translations.