Alberto Leporati

Deterministic solutions to QSAT and Q3SAT by spiking neural P systems with pre-computed resources

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.

Uniform solutions to SAT and Subset Sum by spiking neural P systems

We continue the investigations concerning the possibility of using spiking neural P systems as a framework for solving computationally hard problems, addressing two problems which were already recently considered in this respect:

Simulating the Fredkin gate with energy-based P systems

{\tt Subset}\,{\tt Sum}

Uniform solutions to SAT and 3-SAT by spiking neural P systems with pre-computed resources

and

Sublinear-Space p systems with active membranes

{\tt SAT}.

Membrane Division, Oracles, and the Counting Hierarchy

For both of them we provide uniform constructions of standard spiking neural P systems (i.e., not using extended rules or parallel use of rules) which solve these problems in a constant number of steps, working in a non-deterministic way. This improves known results of this type where the construction was non-uniform, and/or was using various ingredients added to the initial definition of spiking neural P systems (the SN P systems as defined initially are called here “standard”). However, in the