Juan Castellanos

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).

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.

Computing with membranes: P systems with worm-objects

We consider a combination of P systems with objects described by symbols with P systems with objects described by strings. Namely, we work with multisets of strings and consider as the result of a computation the number of strings in a given output membrane. The strings (also called worms) are processed by replication, splitting, mutation, and recombination; no priority among rules and no other ingredient is used. In these circumstances, it is proved that: (1) P systems of this type can generate all recursively enumerable sets of numbers; and moreover, (2) the Hamiltonian Path Problem in a directed graph can be solved in quadratic time, while the SAT problem can be solved in linear time. The interest of the latter result comes from the fact that it is the first time that a polynomial solution to an NP-complete problem has been obtained in the P system framework without making use of the (non-realistic) operation of membrane division.

On the size complexity of hybrid networks of evolutionary processors

The goal of this paper is twofold. Firstly, to survey in a systematic and uniform way the main results regarding the size descriptional complexity measures of hybrid networks of evolutionary processors as generating devices. Secondly, we improve some results about a size measure, prove that it is connected, and discuss the possibility of computing this measure for regular and context-free languages. We also briefly present a few NP-complete problems and recall how they can be solved in linear time by accepting networks of evolutionary processors with linearly bounded resources (nodes, rules, symbols). Finally, the size complexity of accepting hybrid networks of evolutionary processors recognizing all NP languages in polynomial time is briefly discussed.

Optimization of the kernel functions in a probabilistic neural network analyzing the local pattern distribution

This article proposes a procedure for the automatic determination of the elements of the covariance matrix of the gaussian kernel function of probabilistic neural networks. Two matrices, a rotation matrix and a matrix of variances, can be calculated by analyzing the local environment of each training pattern. The combination of them will form the covariance matrix of each training pattern. This automation has two advantages: First, it will free the neural network designer from indicating the complete covariance matrix, and second, it will result in a network with better generalization ability than the original model. A variation of the famous two-spiral problem and real-world examples from the UCI Machine Learning Repository will show a classification rate not only better than the original probabilistic neural network but also that this model can outperform other well-known classification techniques.

Biocircuit design through engineering bacterial logic gates

Designing synthetic biocircuits to perform desired purposes is a scientific field that has exponentially grown over the past decade. The advances in genome sequencing, bacteria gene regulatory networks, as well as the further knowledge of intraspecies bacterial communication through quorum sensing signals are the starting point for this work. Although biocircuits are mostly developed in a single cell, here we propose a model in which every bacterium is considered to be a single logic gate and chemical cell-to-cell connections are engineered to control circuit function. Having one genetically modified bacterial strain per logic process would allow us to develop circuits with different behaviors by mixing the populations instead of re-programming the whole genetic network within a single strain. Two principal advantages of this procedure are highlighted. First, the fully connected circuits obtained where every cellgate is able to communicate with all the rest. Second, the resistance to the noise produced by inappropriate gene expression. This last goal is achieved by modeling thresholds for input signals. Thus, if the concentration of input does not exceed the threshold, it is ignored by the logic function of the gate.

A Binary Data Structure for Membrane Processors: Connectivity Arrays

This paper defines membrane processors as digital processors capable of implementing local processing performed inside membranes in transition P systems. In order to encode the membrane structures of transition P systems, additional binary data structures are needed. Such binary data structures are named ”connectivity arrays”. The main purposes of the connectivity arrays are to distribute information about the system membrane structure among the different processors that implement the transition P system, and to facilitate communication processes among different membrane processors. The information kept in processor has to be versatile and compact; versatile means to easily permit changes in the membrane structure of the system processors, and compact means that not too much memory space is needed.

Accepting splicing systems with permitting and forbidding words

In this paper we propose a generalization of the accepting splicing systems introduced in Mitrana et al. (Theor Comput Sci 411:2414–2422, 2010). More precisely, the input word is accepted as soon as a permitting word is obtained provided that no forbidding word has been obtained so far, otherwise it is rejected. Note that in the new variant of accepting splicing system the input word is rejected if either no permitting word is ever generated (like in Mitrana et al. in Theor Comput Sci 411:2414–2422, 2010) or a forbidding word has been generated and no permitting word had been generated before. We investigate the computational power of the new variants of accepting splicing systems and the interrelationships among them. We show that the new condition strictly increases the computational power of accepting splicing systems. Although there are regular languages that cannot be accepted by any of the splicing systems considered here, the new variants can accept non-regular and even non-context-free languages, a situation that is not very common in the case of (extended) finite splicing systems without additional restrictions. We also show that the smallest class of languages out of the four classes defined by accepting splicing systems is strictly included in the class of context-free languages. Solutions to a few decidability problems are immediately derived from the proof of this result.

Towards an Electronic Implementation of Membrane Computing: A Formal Description of Non-deterministic Evolution in Transition P Systems

This paper is part of a program of our research group, aiming to implement membrane computing on electronic computers. We here present Transition P systems, which is the preliminary steep of our approach. The formalisation we before have in mind the functional programming framework for developing the software modules. Part of these modules has already realised, in Haskell, and they are briefly described in the second section of the paper.

Structures and Bio-language to Simulate Transition P Systems on Digital Computers

The aim of this paper is to show that some computational models inspired from biological membranes, such as P systems, can be simulated on digital computers in an efficient manner. To this aim, it is necessary to characterize non-determinism and parallel execution of evolution rules inside regions. Both these issues are formally described here in order to obtain a feasible description in terms of data structures and operations able to be implemented in a functional programming language. Static and dynamic structures of transition P systems are formalised in order to define a bio-language to represent them. Finally, a draft of a language for describing a transition P systems is presented. It will facilitate the description of transition P systems in terms of sentences in a high level programming language; such sentences will define a program. A process of compilation will parse the program to appropriate data structures and will launch the execution of the simulation process.