Networks of Polarized Evolutionary Processors Are Computationally Complete

Arroyo, Fernando; Canaval, Sandra Gómez; Mitrana, Víctor; Popescu, Sandu

doi:10.1007/978-3-319-04921-2_8

Cited by 16 publications

(9 citation statements)

References 23 publications

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“…The strings that can pass all these subnetworks encode correct colorings and, finally, arrive in the output node. We now recall some results from [5] and [6] concerning the computational power of these networks.…”

Section: Polarization In Network Of Evolutionary Processorsmentioning

confidence: 99%

Polarization: a new communication protocol in networks of bio-inspired processors

Mitrana

2019

J Membr Comput

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This work is a survey of the most recent results regarding the computational power of the networks of bio-inspired processors whose communication is based on a new protocol called polarization. In the former models, the communication amongst processors is based on filters defined by some random-context conditions, namely the presence of some symbols and the absence of other symbols. In the new protocol discussed here, a polarization (negative, neutral, and positive) is associated with each node, while the polarization of data navigating through the network is computed in a dynamical way by means of a valuation function. Consequently, the protocol of communication amongst processors is naturally based on the compatibility between their polarization and the polarization of the data. We consider here three types of bio-inspired processors: evolutionary processors, splicing processors, and multiset processors. A quantitative generalization of polarization (evaluation sets) is also presented. We recall results regarding the computational power of these networks considered as accepting devices. Furthermore, a solution to an intractable problem, namely the 0 / 1 Knapsack problem, based on the networks of splicing processors with evaluation sets considered as problem solving devices, is also recalled. Finally, we discuss some open problems and possible directions for further research in this area.

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Section: Polarization In Network Of Evolutionary Processorsmentioning

confidence: 99%

Polarization: a new communication protocol in networks of bio-inspired processors

Mitrana

2019

J Membr Comput

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“…NPEPP defines its communication protocol based on the polarization concept. This filtering strategy generalizes the protocol defined by networks working over strings [12,13] in such a way that it does work over rectangular pictures. In particular, the polarization is an abstraction of the electric charge (negative, positive or neutral) that may be applied to both pictures and nodes.…”

Section: Introductionmentioning

confidence: 99%

Networks of Picture Processors with Filtering Based on Evaluation Sets as Solvers for Cryptographic Puzzles Based on Random Multivariate Quadratic Equations

et al. 2020

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Networks of picture processors is a massively distributed and parallel computational model inspired by the evolutionary cellular processes, which offers efficient solutions for NP-complete problems. This bio-inspired model computes two-dimensional strings (pictures) using simple rewriting rules (evolutionary operations). The functioning of this model mimics a community of cells (pictures) that are evolving according to these bio-operations via a selection process that filters valid surviving cells. In this paper, we propose an extension of this model that empowers it with a flexible method that selects the processed pictures based on a quantitative evaluation of its content. In order to show the versatility of this extension, we introduce a solver for a cryptographic proof-of-work based on the hardness of finding a solution to a set of random quadratic equations over the finite field F2. This problem is demonstrated to be NP-hard, even with quadratic polynomials over the field F2, when the number of equations and the number of variables are of roughly the same size. The proposed solution runs in O(n2) computational steps for any size (n,m) of the input pictures. In this context, this paper opens up a wide field of research that looks for theoretical and practical solutions of cryptographic problems via software/hardware implementations based on bio-inspired computational models.

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“…Networks of polarized evolutionary processors were considered in [6] (a new version of that paper is going to appear, [5]), and networks of evolutionary processors with elementary polarizations −1, 0, 1 were investigated in [12]. In this paper we consider the same model of networks of evolutionary processors with elementary polarizations −1, 0, 1 as in [12], yet we considerably improve the number of processors (cells) needed to obtain computational completeness from 35 to 7, which makes these results already comparable with those obtained in [1] for hybrid networks of evolutionary processors using permitting and forbidden contexts as filters for the communication of strings between cells.…”

Section: Introductionmentioning

confidence: 99%

Computational Completeness of Networks of Evolutionary Processors with Elementary Polarizations and a Small Number of Processors

Freund

Rogojin

Verlan

2017

Descriptional Complexity of Formal Systems

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Networks of Polarized Evolutionary Processors Are Computationally Complete

Cited by 16 publications

References 23 publications

Polarization: a new communication protocol in networks of bio-inspired processors

Polarization: a new communication protocol in networks of bio-inspired processors

Networks of Picture Processors with Filtering Based on Evaluation Sets as Solvers for Cryptographic Puzzles Based on Random Multivariate Quadratic Equations

Computational Completeness of Networks of Evolutionary Processors with Elementary Polarizations and a Small Number of Processors

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