On the Computational Power of Spiking Neural P Systems

In this paper we study some computational properties of spiking neural P systems. In particular, we show that by using nondeterminism in a slightly extended version of spiking neural P systems it is possible to solve in constant time both the numerical NP-complete problem Subset Sum and the strongly NP-complete problem 3-SAT. Then, we show how to simulate a universal deterministic spiking neural P system with a deterministic Turing machine, in a time which is polynomial with respect to the execution time of the simulated system. Surprisingly, it turns out that the simulation can be performed in polynomial time with respect to the size of the description of the simulated system only if the regular expressions used in such a system are of a very restricted type

Characterizing PSPACE with Shallow Non-Confluent P Systems

In P systems with active membranes, the question of understanding the power of non-confluence within a polynomial time bound is still an open problem. It is known that, for shallow P systems, that is, with only one level of nesting, non-con uence allows them to solve conjecturally harder problems than con uent P systems, thus reaching PSPACE. Here we show that PSPACE is not only a bound, but actually an exact characterization. Therefore, the power endowed by non-con uence to shallow P systems is equal to the power gained by con uent P systems when non-elementary membrane division and polynomial depth are allowed, thus suggesting a connection between the roles of non-confluence and nesting depth

Characterizing PSPACE with Shallow Non-Confluent P Systems

In P systems with active membranes, the question of understanding the power of non-confluence within a polynomial time bound is still an open problem. It is known that, for shallow P systems, that is, with only one level of nesting, non-con uence allows them to solve conjecturally harder problems than con uent P systems, thus reaching PSPACE. Here we show that PSPACE is not only a bound, but actually an exact characterization. Therefore, the power endowed by non-con uence to shallow P systems is equal to the power gained by con uent P systems when non-elementary membrane division and polynomial depth are allowed, thus suggesting a connection between the roles of non-confluence and nesting depth

Time-driven computations in P Systems

It is a well-known fact that the time of execution of a (biochemical) reaction depends on many factors, and, in particular, on the current situation of the whole system. With this motivation in mind, we propose a model of computation based on membrane systems where the various rewriting rules have different times of execution and, moreover, the time of execution of each rule can vary during the computation, depending on the configuration of the whole system (in this sense, the computation is "time-driven"). We show that such systems are universal in a very simple framework: a regular time-mapping suffices to obtain universality for systems with minimal cooperation (one catalyst)

Improving Universality Results on Parallel Enzymatic Numerical P Systems

We improve previously known universality results on enzymatic numerical P systems (EN P systems, for short) working in all-parallel and one-parallel modes. By using a attening technique, we rst show that any EN P system working in one of these modes can be simulated by an equivalent one-membrane EN P system working in the same mode. Then we show that linear production functions, each depending upon at most one variable, su ce to reach universality for both computing modes. As a byproduct, we propose some small deterministic universal enzymatic numerical P systems

Dynamical Probabilistic P Systems: Definitions and Applications

We introduce dynamical probabilistic P systems, a variant where probabilities associated to the rules change during the evolution of the system, as a new approach to the analysis and simulation of the behavior of complex systems. We define the notions for the analysis of the dynamics and we show some applications for the investigation of the properties of the Brusselator (a simple scheme for the Belousov-Zabothinskii reaction), the Lotka-Volterra system and the decay process

On a Paun’s Conjecture in Membrane Systems

We study a P˘aun’s conjecture concerning the unsolvability of NP–complete problems by polarizationless P systems with active membranes in the usual framework, without cooperation, without priorities, without changing labels, using evolution, communication, dissolution and division rules, and working in maximal parallel manner. We also analyse a version of this conjecture where we consider polarizationless P systems working in the minimally parallel manner.Ministerio de Educación y Ciencia TIN2006–13425Junta de Andalucía TIC–58

Size and Power of Extended Gemmating P Pystems

In P systems with gemmation of mobile membranes were ex- amined. It was shown that (extended) systems with eight membranes are as powerful as the Turing machines. Moreover, it was also proved that extended gemmating P systems with only pre-dynamical rules are still computationally complete: in this case nine membranes are needed to obtain this computational power. In this paper we improve the above results concerning the size bound of extended gemmating P systems, namely we prove that these systems with at most ¯ve membranes (with meta-priority relations and without (in=out) communication rules) form a class of universal computing devices, while in the case of extended systems with only pre-dynamical rules six membranes are enough to determine any recursively enumerable language

Complete Problems for a Variant of P Systems with Active Membranes

We identify a family of decision problems that are hard for some complexity classes defined in terms of P systems with active membranes working in polynomial time. Furthermore, we prove the completeness of these problems in the case where the systems are equipped with a form of priority that linearly orders their rules. Finally, we highlight some possible connections with open problems related to the computational complexity of P systems with active membranes

Introducing a Space Complexity Measure for P Systems

We define space complexity classes in the framework of membrane computing, giving some initial results about their mutual relations and their connection with time complexity classes, and identifying some potentially interesting problems which require further research