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

Connection between the Slave-Particles and X-Operators Path-Integral Representations. a New Perturbative Approach

In the present work it is shown that the family of first-order Lagrangians for the t-J model and the corresponding correlation generating functional previously found can be exactly mapped into the slave-fermion decoupled representation. Next, by means of the Faddeev-Jackiw symplectic method, a different family of Lagrangians is constructed and it is shown how the corresponding correlation generating functional can be mapped into the slave-boson representation. Finally, in order to define the propagation of fermion modes we discuss two alternative ways to treat the fermionic sector in the path-integral formalism for the t-J model.Comment: 27 pages, latex, no figures(to be published in Journal of Physics A:Mathematical and General

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

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

Simulating counting oracles with cooperation

We prove that monodirectional shallow chargeless P systems with active membranes and minimal cooperation working in polynomial time precisely characterise P#P k , the complexity class of problems solved in polynomial time by deterministic Turing machines with a polynomial number of parallel queries to an oracle for a counting problem

Non-confluence in divisionless P systems with active membranes

AbstractWe describe a solution to the SAT problem via non-confluent P systems with active membranes, without using membrane division rules. Furthermore, we provide an algorithm for simulating such devices on a nondeterministic Turing machine with a polynomial slowdown. Together, these results prove that the complexity class of problems solvable non-confluently and in polynomial time by this kind of P system is exactly the class NP

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