Claudio Ferretti

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.

Solving numerical NP-complete problems with spiking neural P systems

Starting from an extended nondeterministic spiking neural P system that solves the Subset SUM problem in a constant number of computation 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 prove that this conversion cannot be performed in polynomial time if the use of maximal parallelism is forbidden. Finally, we show that if we can choose whether each neuron works in the nondeterministic vs. deterministic and/or in the maximal parallel vs. sequential way, then there exists a uniform family of spiking neural P systems that solves the SUBSET SUM problem.

On three variants of rewriting P systems

We continue here the study of P systems with string objects processed by rewriting rules, by investigating some questions which are classic in formal language theory: leftmost derivation, conditional use of rules (permitting and forbidding conditions), relationships with language families in Chomsky and Lindenmayer hierarchies.

Word Design for Molecular Computing: A Survey

This paper gives a short survey, and a reading grid, of results about the coding problem of molecular design.

Separating some splicing models

Abstract In this paper we show that the three main definitions of the splicing operation known in the literature, i.e., the Head [Bull. Math. Biology 49 (1987) 737–759], Paun [Theoret. Comput. Sci. 168 (1996) 321–326] and Pixton [Discrete Appl. Math. 69 (1996) 101–124] definitions, give rise to different subclasses of regular languages, when a finite set of rules is iterated on a finite set of axioms. More precisely, we show that the family of regular languages generated by finite splicing, as defined in the early paper by Head, is strictly included in the family defined later by Paun, which is in turn strictly included in the splicing family defined by Pixton. We describe instance languages in the difference sets, and we prove that they cannot be generated by the smaller families.

Parallel Rewriting P Systems with Deadlock

We analyze P systems with different parallel methods for string rewriting. The notion of deadlock state is introduced when some rules with mixed target indications are simultaneously applied on a common string. The computational power of systems with and without deadlock is analyzed and a lower bound for the generative power is given, for some parallelism methods. Some open problems are also formulated.

Complexity aspects of polarizationless membrane systems

We investigate polarizationless P systems with active membranes working in maximally parallel manner, which do not make use of evolution or communication rules, in order to find which features are sufficient to efficiently solve computationally hard problems. We show that such systems are able to solve the PSPACE-complete problem Quantified 3-sat, provided that non-elementary membrane division is controlled by the presence of a (possibly non-elementary) membrane.

A Reduced Distributed Splicing System for RE Languages

In this paper we prove that each recursively enumerable language can be generated using a distributed splicing system with a fixed number of test tubes. This improves a recent result by Csuhaj-Varju, Kari, Păun, proving computational completeness only for a system with a number of tubes depending on the cardinality of the used alphabet.

Computing with energy and chemical reactions

Taking inspiration from some laws of Nature—energy transformation and chemical reactions—we consider two different paradigms of computation in the framework of Membrane Computing. We first study the computational power of energy-based P systems, a model of membrane systems where a fixed amount of energy is associated with each object and the rules transform objects by manipulating their energy. We show that if we assign local priorities to the rules, then energy-based P systems are as powerful as Turing machines; otherwise, they can be simulated by vector addition systems, and hence are not universal. Then, we consider stochastic membrane systems where computations are performed through chemical networks. We show how molecular species and chemical reactions can be used to describe and simulate the functioning of Fredkin gates and circuits. We conclude the paper with some research topics related to computing with energy-based P systems and with chemical reactions.

A membrane computing system mapped on an asynchronous, distributed computational environment

We show how to simulate a membrane system on a (simulated) distributed and bio-inspired computational architecture (BME). The advantages of this approach are the ease of representing each membrane with a processing element and the perspective of exploiting the expected nano-technological implementation of such an architecture. By combining these two non-conventional computing architectures, we touch interesting subproblems, such as the trade-off between being synchronous (P systems) and asynchronous (BME), or between structural adjacency and position-independent communications.