Networks Of Evolutionary Processors Research Articles

Networks of evolutionary processors: wheel graph simulation

Networks of evolutionary processors: wheel graph simulation

Simulations between Network Topologies in Networks of Evolutionary Processors

In this paper, we propose direct simulations between a given network of evolutionary processors with an arbitrary topology of the underlying graph and a network of evolutionary processors with underlying graphs—that is, a complete graph, a star graph and a grid graph, respectively. All of these simulations are time complexity preserving—namely, each computational step in the given network is simulated by a constant number of computational steps in the constructed network. These results might be used to efficiently convert a solution of a problem based on networks of evolutionary processors provided that the underlying graph of the solution is not desired.

Simulating polarization by random context filters in networks of evolutionary processors

Networks of evolutionary processors (NEP for short) form a class of models within the new computational paradigms inspired by biological phenomena. They are known to be theoretically capable of solving intractable problems. So far, there are two main categories that differ from each other by the nature of filtering process controlling the communication step: random-context clauses or polarization. Several studies have proven that both of them are computationally complete through efficient simulations of universal computational models such as Turing machines and 2-tag systems. Nevertheless, the indirect conversion between the two network variants results in an exponential increase of the computational complexity. In this paper, we suggest a direct simulation of polarized NEP through NEP with random-context filters which incurs in lower complexity costs.

Developing Tools for Networks of Processors

A great deal of research eort is currently being made in the realm of so called natural computing. Natural computing mainly focuses on the denition, formal description, analysis, simulation and programming of new models of computation (usually with the same expressive power as Turing Machines) inspired by Nature, which makes them particularly suitable for the simulation of complex systems.Some of the best known natural computers are Lindenmayer systems (Lsystems, a kind of grammar with parallel derivation), cellular automata, DNA computing, genetic and evolutionary algorithms, multi agent systems, arti- cial neural networks, P-systems (computation inspired by membranes) and NEPs (or networks of evolutionary processors). This chapter is devoted to this last model.

Networks of Bio-inspired Processors

The goal of this work is twofold. Firstly, we propose a uniform view of three types of accepting networks of bio-inspired processors: networks of evolutionary processors, networks of splicing processors and networks of genetic processors. And, secondly, we survey some features of these networks: computational power, computational and descriptional complexity, the existence of universal networks, eciency as problem solvers and the relationships among them.

Solving optimization problems by using networks of evolutionary processors with quantitative filtering

Searching for new efficient algorithms to solve complex optimization problems in big data scenarios is a priority, especially when the search space increases exponentially with the problem size, making impossible to find a solution through a mere blind search. Networks of Evolutionary Processors (NEP) is a formal framework formed of highly parallel and distributed computing models inspired and abstracted from biological evolution that is able to solve hard problems in an efficient way. However, NEP is not expressive enough to model quantitative aspects present in many problems. In this paper we propose NEPO, a new model based on the NEP evolutionary processors. NEPO deals with a class of data that is able to solve hard optimization problems and defines a novel selection process based on a quantitative filtering strategy. We present a linear time solution to a well known NP-complete optimization problem (the 0/1 Knapsack problem) in order to demonstrate NEPO advantages. This result suggests that NEPO's quantitative filtering is more suitable to tackle practical solutions to optimization problems in order to deploy them on highly scalable distributed computational platforms.

Computational completeness of complete, star-like, and linear hybrid networks of evolutionary processors with a small number of processors

A hybrid network of evolutionary processors (HNEP) is a graph where each node is associated with a special rewriting system called an evolutionary processor, an input filter, and an output filter. Each evolutionary processor is given a finite set of one type of point mutations (insertion, deletion or a substitution of a symbol) which can be applied to certain positions in a string. An HNEP rewrites the strings in the nodes and then re-distributes them according to a filter-based communication protocol; the filters are defined by certain variants of random-context conditions. HNEPs can be considered both as languages generating devices (GHNEPs) and language accepting devices (AHNEPs); most previous approaches treated the accepting and generating cases separately. For both cases, in this paper we show that five nodes are sufficient to accept (AHNEPs) or generate (GHNEPs) any recursively enumerable language by showing the more general result that any partial recursive relation can be computed by an HNEP with (at most) five nodes with the underlying graph structure for the communication between the evolutionary processors being the complete or the linear graph with five nodes, whereas with a star-like communication graph we need six nodes. If the final results are defined by only taking the terminal strings out of the designated output node, then for these extended HNEPs we can prove that only four nodes are needed in all cases--for computing any partial recursive relation as well as for generating and accepting any recursively enumerable language--and the underlying communication structure can be a complete or a linear graph, but now even a star-like graph, too.

Towards a Bio-Inspired Theoretical Linguistics to Model Man-Machine Communication

The paper provides an overview of what could be a new biological-inspired linguistics. The authors discuss some reasons for attempting a more natural description of natural language, lying on new theories of molecular biology and their formalization within the area of theoretical computer science. The authors especially explore three bio-inspired models of computation –DNA computing, membrane computing and networks of evolutionary processors (NEPs) – and their possibilities for achieving a simpler, more natural, and mathematically consistent theoretical linguistics.

Networks of evolutionary processors: the power of subregular filters

In this paper, we propose a hierarchy of families of languages generated by networks of evolutionary processors where the filters belong to several special classes of regular sets. More precisely, we show that the use of filters from the class of ordered, non-counting, power-separating, circular, suffix-closed regular, union-free, definite, and combinational languages is as powerful as the use of arbitrary regular languages and yields networks that can generate all the recursively enumerable languages. On the other hand, the use of filters that are only finite languages allows only the generation of regular languages, but not every regular language can be generated. If we use filters that are monoids, nilpotent languages, or commutative regular languages, we obtain one and the same family of languages which contains non-context-free languages but not all regular languages. These results seem to be of interest because they provide both upper and lower bounds on the families of languages that one can use as filters in a network of evolutionary processors in order to obtain a complete computational model.

Networks of evolutionary processors: computationally complete normal forms

Networks of evolutionary processors (NEPs, for short) form a bio-inspired language generating computational model that was shown to be equivalent to the model of phrase-structure grammars. In this paper, we analyse different restricted variants of NEPs that preserve the computational power of the general model. We prove that any recursively enumerable language can be generated by a NEP where the derivation rules can be applied at arbitrarily chosen positions, the control of the communication is done by finite automata with at most three states, and either the rule sets are singletons or the underlying graph is a complete graph. If one uses networks with arbitrary underlying graphs and allows the additional application of insertions and deletions only to the right-most or the to left-most position of the derived words for some nodes, then we only need automata with only one state to control the communication in the network. Clearly, this result is optimal; moreover, finite automata with two states are necessary and sufficient in order to generate all the recursively enumerable languages when the derivation rules can be applied only at arbitrarily chosen positions.

Accepting Networks of Genetic Processors are computationally complete

We propose a computational model that is inspired by genetic operations over strings such as mutation and crossover. The model, Accepting Network of Genetic Processors, is highly related to previously proposed ones such as Networks of Evolutionary Processors and Networks of Splicing Processors. These models are complete computational models inspired by DNA evolution and recombination. Here, we prove that the proposed model is computationally complete (it is equivalent to the Turing machine). Hence, it can accept any recursively enumerable language. In addition, we relate the proposed model with (parallel) Genetic Algorithms or Evolutionary Programs and we set these techniques as decision problem solvers.

Biocomputing: an insight from linguistics

This paper is placed in a formal framework in which the interdisciplinary study of natural language is conducted by integrating linguistics, computer science and biology. It provides an overview of the field of research, conveying the main biological ideas that have influenced research in linguistics. Our work highlights the main methods of molecular computing that have been applied to the processing and study of the structure of natural language: DNA computing, membrane computing and networks of evolutionary processors. Moreover, some new challenges and lines of research for the future are pointed out, that can provide important improvements in the understanding of natural language as a structure and a human capacity.

Complexity-preserving simulations among three variants of accepting networks of evolutionary processors

In this paper we consider three variants of accepting networks of evolutionary processors. It is known that two of them are equivalent to Turing machines. We propose here a direct simulation of one device by the other. Each computational step in one model is simulated in a constant number of computational steps in the other one while a translation via Turing machines squares the time complexity. We also discuss the possibility of constructing simulations that preserve not only complexity, but also the shape of the simulated network.

FILTER POSITION IN NETWORKS OF SUBSTITUTION PROCESSORS DOES NOT MATTER

It is known ([4]) that moving the filters from the nodes to the edges in accepting hybrid networks of evolutionary processors does not decrease the computational power of the model which equals that of a Turing machine. A direct and time complexity preserving simulation is presented in [1]. All three types of processors (substitution, insertion, deletion) are essentially used in this simulation. In this note we prove that such a direct simulation between networks containing substitution nodes only still exists.

Target Based Accepting Networks of Evolutionary Processors

In this paper, a new definition of accepting networks - called target based accepting networks - is given. In a target based accepting network of evolutionary processors, each node is equipped with a target condition. As soon as a node contains a word which satisfies the target condition of that node, the input word is accepted by the network. In this way, no further output nodes are necessary. Regarding the communication in a network, we consider two cases of control: 1. input and output filters are regular languages, then the target conditions are to belong to certain regular languages, 2. input and output filters are implemented as random context conditions, then the target conditions are given by sets of permitting and forbidding symbols. It is shown in both cases that conventional accepting networks and target based accepting networks have the same computational power. However, the number of processors needed for accepting a language can be reduced when using target based networks.

Breaking the data encryption standard using networks of evolutionary processors with parallel string rewriting rules

In this paper we introduce a biologically inspired distributed computing model called networks of evolutionary processors with parallel string rewriting rules (NEPPS), which is a variation of the hybrid networks of evolutionary processors introduced by Martin-Vide et al. Such a network contains simple processors that are located in the nodes of a virtual graph. Each processor has strings (each string having multiple copies) and string rewriting rules. The rules are applied parallely on the strings. After the strings have been rewritten, they are communicated among the processors through filters. We show that we can theoretically break the DES (data encryption standard), which is the most widely used cryptosystem, using NEPPS. We prove that, given an arbitrary <plain-text, cipher-text> pair, one can recover the DES key in a constant number of steps.

Networks of Evolutionary Processors: A Survey

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ON THE DESCRIPTIONAL COMPLEXITY OF ACCEPTING NETWORKS OF EVOLUTIONARY PROCESSORS WITH FILTERED CONNECTIONS

In this paper we consider, from the descriptional complexity point of view, a model of computation introduced in [1], namely accepting network of evolutionary processors with filtered connections (ANEPFCs). First we show that for each morphism h : V → W*, with V ∩ W = ∅, one can effectively construct an ANEPFC, of size 6 + |W|, which accepts every input word w and, at the end of the computation on this word, obtains h(w) in its output node. This result can be applied in constructing two different ANEPFCs, with 27 and, respectively, 26 processors, recognizing a given recursively enumerable language. The first architecture, based on the construction of a universal ANEPFC, has the property that only 7 of its 27 processors depend on the accepted language. On the other hand, all the 26 processors of the second architecture depend on the accepted language, but, differently from the first one, this network simulates efficiently (from both time and space perspectives) a nondeterministic Turing machine accepting the given language.

On the recognition of context-free languages using accepting hybrid networks of evolutionary processors

In this paper we approach the problem of constructing an accepting device for the class of context-free languages, based on a newly defined computational model: Accepting Hybrid Network of Evolutionary Processors (AHNEPs). Although it is known that AHNEPs are Turing complete, and, consequently, for every context-free language, seen as a recursively enumerable language, we can construct an AHNEP that simulates the Turing machine accepting it, we choose a direct approach: the AHNEPs we design simulate the computation done by a non-deterministic push-down automata accepting the language. This approach leads to a more economic AHNEP since the number of processors we use depends linearly on the number of states and the number of working symbols of the automaton, while for the network obtained in the general case of recursively enumerable languages, the number of processors is linear in the number of states, but quadratic in the number of working symbols of a Turing machine accepting the given language. Finally, we particularize the AHNEP architecture we proposed in order to recognize regular languages. We obtain an upper bound for the number of processors needed close to that known for generating hybrid networks of evolutionary processors.

On the number of nodes in universal networks of evolutionary processors

We consider the networks of evolutionary processors (NEP) introduced by J. Castellanos, C. Marti n-Vide, V. Mitrana and J. Sempere recently. We show that every recursively enumerable (RE) language can be generated by an NEP with three nodes modulo a terminal alphabet and moreover, NEPs with four nodes can generate any RE language. Thus, we improve existing universality result from five nodes down to four nodes. For mNEPs (a variant of NEPs where operations of different kinds are allowed in the same node) we obtain optimal results: each RE language can be generated by an mNEP with one node modulo a terminal alphabet, and mNEPs with two nodes can generate any RE language; this is not possible for mNEPs with one node. Some open problems are formulated.