Abstract
Among 
-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 
. 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 
, 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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Leporati, A., Manzoni, L., Mauri, G., Porreca, A.E., Zandron, C. (2019). Solving QSAT in Sublinear Depth. In: Hinze, T., Rozenberg, G., Salomaa, A., Zandron, C. (eds) Membrane Computing. CMC 2018. Lecture Notes in Computer Science(), vol 11399. Springer, Cham. https://doi.org/10.1007/978-3-030-12797-8_13
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