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 nlog n, where n is the number of variables in the quantified formula given as input.
Leporati, A., Manzoni, L., Mauri, G., Porreca, A., Zandron, C. (2019). Solving QSAT in Sublinear Depth. In Membrane Computing 19th International Conference, CMC 2018, Dresden, Germany, September 4–7, 2018, Revised Selected Papers (pp.188-201). Springer Nature Switzerland [10.1007/978-3-030-12797-8_13].
Solving QSAT in Sublinear Depth
Leporati, A;Manzoni, L;Mauri, G;Porreca, AE;Zandron, C
2019
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 nlog n, where n is the number of variables in the quantified formula given as input.
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