Solving QSAT in sublinear depth

Alberto Leporati; Luca Manzoni; Giancarlo Mauri; Antonio E. Porreca; Claudio Zandron

doi:10.1007/978-3-030-12797-8_13

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arXiv · 1902.03879

Solving QSAT in sublinear depth

Alberto Leporati·Luca Manzoni·Giancarlo Mauri·Antonio E. Porreca·Claudio Zandron

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Abstract

Among $\mathbf{PSPACE}$-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 $\mathbf{PSPACE}$. 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 $\mathbf{P^{\#P}}$, 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 $\frac{n}{\log n}$, where $n$ is the number of variables in the quantified formula given as input.

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Alberto Leporati, Luca Manzoni, Giancarlo Mauri, Antonio E. Porreca, Claudio Zandron. 2019-02-11. Solving QSAT in sublinear depth. https://doi.org/10.1007/978-3-030-12797-8_13

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