Hybrid Networks of Evolutionary Processors

Abstract

Abstract.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.

On the size complexity of hybrid networks of evolutionary processors

“…In the theory of networks some types of underlying graphs are common, e.g., rings, stars, grids, etc. In some of the aforementioned papers [3,5,17,15], there were investigated networks of evolutionary processors having underlying graphs of these special forms, but with a special attention to complete graphs. Thus a GHNEP (AHNEP) is said to be a star, ring, grid, or complete GHNEP (AHNEP) if its underlying graph is a star, ring, grid, or complete graph, respectively.…”

“…Moreover, the rules are applied in the same manner in all the nodes. These restrictions are discarded in [17] and [15]. By this reason, these networks are called hybrid.…”

Networks of Polarized Evolutionary Processors Are Computationally Complete

“…NEPs as language generating devices and problem solvers have been considered in [2] and [14], respectively. They have been further investigated in a series of subsequent works.…”

PNEPs, NEPs for Context Free Parsing: Application to Natural Language Processing

“…NEP as a generating device was first introduced in [11] and [12]. The topic is further investigated in [13], while further different variants of the generating machine are introduced and analyzed in [14][15][16][17][18].…”

“…Other authors have previously studied the relationships between NEPs, regular, context-free, and recursively enumerable languages [14][15][16][17][18]. [21] shows how NEPs simulate the application of context free rules (A → α, A ∈ V, α ∈ V * for alphabet V ): a set of additional nodes is needed to implement a rather complex technique to rotate the string and locate A in one of the string ends, then delete it and adding all the symbols in α. PNEPs use context free rules rather than classic substitution (A → B, A, B ∈ V ), as well as insertion and deletion NEP rules.…”