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In this paper we continue previous studies on the computational efficiency of spiking neural P systems, under the assumption that some pre-computed resources of exponential size are given in advance. Specifically, we give a deterministic solution for each of two well known
PSPACE-complete problems:
QSAT and
Q3SAT. In the case of
QSAT, the answer to any instance of the problem is computed in a time which is linear with respect to both the number
n
of Boolean variables and the number
m
of clauses that compose the instance. As for
Q3SAT, the answer is computed in a time which is at most cubic in the number
n
of Boolean variables.