Complexity Issues in Finding Succinct Solutions of PSPACE-Complete Problems

TL;DR

This paper explores the complexity of determining whether PSPACE-complete problems have succinct models of bounded size, highlighting differences from NP problems and examining the complexity of such decision problems.

Contribution

It analyzes the complexity of deciding the existence of polynomially succinct models for PSPACE-complete problems with size bounds, a less understood aspect compared to NP problems.

Findings

Models of PSPACE-complete problems can be exponentially large but may have polynomial space succinct representations.

Deciding the existence of succinct models of bounded size in PSPACE-complete problems is computationally complex.

The paper provides complexity results for the problem of finding succinct models within size bounds.

Abstract

We study the problem of deciding whether some PSPACE-complete problems have models of bounded size. Contrary to problems in NP, models of PSPACE-complete problems may be exponentially large. However, such models may take polynomial space in a succinct representation. For example, the models of a QBF are explicitely represented by and-or trees (which are always of exponential size) but can be succinctely represented by circuits (which can be polynomial or exponential). We investigate the complexity of deciding the existence of such succinct models when a bound on size is given.