Abstract
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.
Highlights
Networks of bio-inspired processors (NBP) is a family of computational models facing NP-complete problems by mimicking, from a syntactical perspective, the manner by which cell communities evolve via gene mutations in DNA molecules
A complete coefficient-based representation of all polynomials in the equation system requires log(q) · m · (n · (n − 1)/2 + n + 1) bits in a classical computer. Another contribution of this paper is that we construct a solver based on network of picture processors with evaluation sets (NPPES) for solving an instance of the multivariate quadratic (MQ) problem, assuming the polynomials P(1) (x), P(2) (x), . . . , P(n−8) (x) are given in a special form. We introduce such solver based on NPPES, which is able to find a vector x = ( x1, . . . , xn )
We have introduced a solver for the random multivariate quadratic equations (RMQE) problem that is based on NPPES and runs in quadratic time, suggesting that the NPPES model can be employed to cope with hard complex problems in which numerical evaluation has an essential role
Summary
Networks of bio-inspired processors (NBP) is a family of computational models facing NP-complete problems by mimicking, from a syntactical perspective, the manner by which cell communities evolve via gene mutations in DNA molecules. An NPP model named networks of polarized evolutionary picture processors (NPEPP) was proposed in [11]. 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. A generalization of the polarization concept using evaluation sets to enhance the valuation mapping to calculate the exact value ( the sign of this value) was proposed in [14] and was used to empower the network of splicing processors [15] and the networks of evolutionary processors [16] models.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
