Claudio Zandron

Solving NP-Complete Problems Using P Systems with Active Membranes

A recently introduced variant of P-systems considers membranes which can multiply by division. These systems use two types of division: division for elementary membranes (Le. membranes not containing other membranes inside) and division for non-elementary membranes. In two recent papers it is shown how to solve the Satisfiability problem and the Hamiltonian Path problem (two well known NP complete problems) in linear time with respect to the input length, using both types of division. We show in this paper that P-systems with only division for elementary membranes suffice to solve these two problems in linear time. Is it possible to solve NP complete problems in polynomial time using P-systems without membrane division? We show, moreover, that (if P ≠ NP) deterministic P-systems without membrane division are not able to solve NP complete problems in polynomial time.

DYNAMICAL PROBABILISTIC P SYSTEMS

Dynamical probabilistic P systems are discrete, stochastic, and parallel devices, where the probability values associated with the rules change during the evolution of the system. These systems are proposed as a novel approach to the analysis and simulation of the behavior of complex systems. We introduce all necessary definitions of these systems and of their dynamical aspects, we describe the functioning of the parallel and stochastic algorithm used in computer simulation, and evaluate its time complexity. Finally, we show some applications of dynamical probabilistic P systems for the investigation of the dynamics of the Lotka-Volterra system and of metapopulation systems.

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}

Analysis and simulation of dynamics in probabilistic p systems

and

P systems with input in binary form

{\tt SAT}.