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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: Subset Sum and SAT: 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 Subset Sum case, a price to pay for this improvement is that the solution is obtained either in a time which depends on the value of the numbers involved in the problem, or by using a system whose size depends on the same values, or again by using complicated regular expressions. A uniform solution to 3-SAT is also provided, that works in constant time.

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.

Starting from an extended nondeterministic spiking neural P system that solves the Subset Sum problem in a constant number of steps, recently proposed in a previous paper, we investigate how different properties of spiking neural P systems affect the capability to solve numerical NP-complete problems. In particular, we show that by using maximal parallelism we can convert any given integer number from the usual binary notation to the unary form, and thus we can initialize the above P system with the required (exponential) number of spikes in polynomial time. On the other hand, we show that this conversion cannot be performed in polynomial time if the use of maximal parallelism is forbidden. Finally, we show that by selectively using nondeterminism and maximal parallelism (that is, for each neuron in the system we can specify whether it works in deterministic or nondeterministic way, as well as in sequential or maximally parallel way) there exists a uniform spiking neural P system that solves all the instances of Subset Sum of a given size.

Summary. We investigate the influence that the flow of information in membrane systems has on their computational complexity. In particular, we analyse the behaviour of P systems with active membranes where communication only happens from a membrane towards its parent, and never in the opposite direction. We prove that these "monodirectional P systems" are, when working in polynomial time and under standard complexity-theoretic assumptions, much less powerful than unrestricted ones: indeed, they characterise classes of problems defined by polynomial-time Turing machines with NP oracles, rather than the whole class PSPACE of problems solvable in polynomial space.