Carlos Martín-Vide

Tissue P systems

Starting from the way the inter-cellular communication takes place by means of protein channels (and also from the standard knowledge about neuron functioning), we propose a computing model called a tissue P system, which processes symbols in a multiset rewriting sense, in a net of cells. Each cell has a finite state memory, processes multisets of symbol-impulses, and can send impulses (“excitations”) to the neighboring cells. Such cell nets are shown to be rather powerful: they can simulate a Turing machine even when using a small number of cells, each of them having a small number of states. Moreover, in the case when each cell works in the maximal manner and it can excite all the cells to which it can send impulses, then one can easily solve the Hamiltonian Path Problem in linear time. A new characterization of the Parikh images of ET0L languages is also obtained in this framework. Besides such basic results, the paper provides a series of suggestions for further research.

Networks of evolutionary processors

Abstract. In this paper we consider networks of evolutionary processors as language generating and computational devices. When the filters are regular languages one gets the computational power of Turing machines with networks of size at most six, depending on the underlying graph. When the filters are defined by random context conditions, we obtain an incomparability result with the families of regular and context-free languages. Despite their simplicity, we show how the latter networks might be used for solving an NP-complete problem, namely the “3-colorability problem”, in linear time and linear resources (nodes, symbols, rules).

A New Class of Symbolic Abstract Neural Nets: Tissue P Systems

Starting from the way the inter-cellular communication takes place by means of protein channels and also from the standard knowledge about neuron functioning, we propose a computing model called a tissue P system, which processes symbols in a multiset rewriting sense, in a net of cells similar to a neural net. Each cell has a finite state memory, processes multisets of symbol-impulses, and can send impulses (?excitations?) to the neighboring cells. Such cell nets are shown to be rather powerful: they can simulate a Turing machine even when using a small number of cells, each of them having a small number of states. Moreover, in the case when each cell works in the maximal manner and it can excite all the cells to which it can send impulses, then one can easily solve the Hamiltonian Path Problem in linear time. A new characterization of the Parikh images of ET0L languages are also obtained in this framework.

Solving NP-Complete Problems With Networks of Evolutionary Processors

We propose a computational device based on evolutionary rules and communication within a network, similar to that introduced in [4], called network of evolutionary processors. An NP-complete problem is solved by networks of evolutionary processors of linear size in linear time. Some furher directions of research are finally discussed.

Solving multidimensional 0--1 knapsack problem by P systems with input and active membranes

Membrane systems are biologically motivated theoretical models of distributed and parallel computing. In this paper, we present a membrane algorithm to solve multidimensional 0-1 knapsack problem in linear time by recognizer P systems with input and with active membranes using 2-division. This algorithm can also be modified to solve general 0-1 integer programming problem.

Hybrid networks of evolutionary processors

A hybrid network of evolutionary processors consists of several processors which are placed in nodes of a virtual graph and can perform one simple operation only on the words existing in that node in accordance with some strategies. Then the words which can pass the output filter of each node navigate simultaneously through the network and enter those nodes whose input filter was passed. We prove that these networks with filters defined by simple random-context conditions, used as language generating devices, are able to generate all linear languages in a very efficient way, as well as non-context-free languages. Then, when using them as computing devices, we present two linear solutions of the Common Algorithmic Problem.

Membrane systems with promoters/inhibitors

Abstract. The computational model of membrane computing (formalized through membrane systems, also called P systems) is based on the way that biological membranes define compartments, each having its set of molecules and (enzymes enhancing) reactions, with compartments communicating through the transport of molecules through membranes. In this paper we augment the basic model of membrane systems with promoters and inhibitors, which formalize the reaction enhancing and reaction prohibiting roles of various substances (molecules) present in cells. We formalize such membrane systems with promoters/inhibitors and investigate their basic properties. In particular we establish universality results, i.e., we provide characterizations of recursively enumerable sets (of vectors of natural numbers) using these systems. It turns out that systems with promoters/inhibitors achieve universal computations without using the standard “auxiliary” features of membrane systems, for instance, without using catalysts.

Special Issue on Second International Conference on the Theory and Practice of Natural Computing, TPNC 2013

This special issue of the journal ‘Soft Computing—AFusion of Foundations, Methodologies and Applications’ offers extended versions of some of the best papers presented at the Second International Conference on the Theory and Practice of Natural Computing, TPNC 2013, held in Caceres, Spain, on December 3–5, 2013, under the organisation of the Research Group on Mathematical Linguistics (GRLMC) from Rovira i Virgili University in Tarragona, Spain and the Computer Architecture and Logic Design Group (ARCO) from University of Extremadura, Spain. TPNC 2013 was the second event in a series dedicated to host and promote research in a wide spectrum of computational models, methods and techniques inspired by information processing in nature. We encouraged both theoretical contributions in soft computing, computing architectures, and formal models as well as solutions for practical problems based on natural computing methods. Out of 47 submissions to the conference, 18 papers were accepted (which represents a competitive acceptance rate of about 38 %). Among them, the authors of 13 papers were invited to submit to this special issue. Each submission was reviewed by at least two experts and, on the basis of their comments, the guest editors decided to accept six papers for this special issue (which represents an acceptance rate of about 13 % out of the submissions to the conference).

Characterizations of recursively enumerable languages by means of insertion grammars

Abstract An insertion grammar is based on pure rules of the form uv → uxv (the string x is inserted in the context (u, v)). A strict subfamily of the context-sensitive family is obtained, incomparable with the family of linear languages. We prove here that each recursively enumerable language can be written as the weak coding of the image by an inverse morphism of a language generated by an insertion grammar (with the maximal length of strings u, v as above equal to seven). This result is rather surprising in view of some closure properties established earlier in the literature. Some consequences of this result are also stated. When also erasing rules of the form uxv → uv are present (the string x is erased from the context (u, v)), then a much easier representation of recursively enumerable languages is obtained, as the intersection with V ∗ of a language generated by an insertion grammar with erased strings (having the maximal length of strings u, v as above equal to two).

Hybrid networks of evolutionary processors are computationally complete

Abstract.A hybrid network of evolutionary processors (an HNEP) consists of several language processors which are located in the nodes of a virtual graph and able to perform only one type of point mutations (insertion, deletion, substitution) on the words found in that node, according to some predefined rules. Each node is associated with an input and an output filter, defined by some random-context conditions. After applying in parallel a point mutation to all the words existing in every node, the new words which are able to pass the output filter of the respective node navigate simultaneously through the network and enter those nodes whose input filter they are able to pass. We show that even the so-called elementary HNEPs are computationally complete. In this case every node is able to perform only one instance of the specified operation: either an insertion, or a deletion, or a substitution of a certain symbol. We also prove that in the case of non-elementary networks, any recursively enumerable language over a common alphabet can be obtained with an HNEP whose underlying structure is a fixed graph depending on the common alphabet only.