Complexity Issues in Finding Succinct Solutions of PSPACE-Complete Problems

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.