Solving QSAT in Sublinear Depth

Abstract

Among PSPACE-complete problems, QSAT, or quantified SAT, is one of the most used to show that the class of problems solvable in polynomial time by families of a given variant of P systems includes the whole PSPACE. However, most solutions require a membrane nesting depth that is linear with respect to the number of variables of the QSAT instance under consideration. While a system of a certain depth is needed, since depth 1 systems only allows to solve problems in P#P, it was until now unclear if a linear depth was, in fact, necessary. Here we use P systems with active membranes with charges, and we provide a construction that proves that QSAT can be solved with a sublinear nesting depth of order n/log n, where n is the number of variables in the quantified formula given as input.