# Knowledge compilation languages as proof systems

## TL;DR

This paper explores how knowledge compilation languages like decision DNNF can be adapted as proof systems for higher complexity problems such as #SAT and maxSAT, extending the framework beyond coNP.

## Contribution

It demonstrates how to modify existing knowledge compilation languages to serve as proof systems for problems in the polynomial hierarchy, specifically #SAT and maxSAT.

## Key findings

- Decision DNNF can be used as proof systems for #SAT and maxSAT.
- The approach extends Cook-Reckhow proof systems to higher complexity classes.
- Framework provides new tools for certifying solutions in complex problems.

## Abstract

In this paper, we study proof systems in the sense of Cook-Reckhow for problems that are higher in the polynomial hierarchy than coNP, in particular, #SAT and maxSAT. We start by explaining how the notion of Cook-Reckhow proof systems can be apply to these problems and show how one can twist existing languages in knowledge compilation such as decision DNNF so that they can be seen as proof systems for problems such as #SAT and maxSAT.