On the size of computationally complete hybrid networks of evolutionary processors

Abstract

a b s t r a c tA hybrid network of evolutionary processors (an HNEP) is a graph where each node is associated with an evolutionary processor (a special rewriting system), a set of words, an input filter and an output filter. Every evolutionary processor is given with a finite set of one type of point mutations (an insertion, a deletion or a substitution of a symbol) which can be applied to certain positions of a string over the domain of the set of these rewriting rules. The HNEP functions by rewriting the words that can be found at the nodes and then re-distributing the resulting strings according to a communication protocol based on a filtering mechanism. The filters are defined by certain variants of random-context conditions. HNEPs can be considered as both language generating devices (GHNEPs) and language accepting devices (AHNEPs). In this paper, by improving the previous results, we prove that any recursively enumerable language can be determined by a GHNEP and an AHNEP with 7 nodes. We also show that the families of GHNEPs and AHNEPs with 2 nodes are not computationally complete.

Networks of Evolutionary Processors with Subregular Filters

“…If one restricts the networks to be without loops (as usual in the literature, e. g., [1]), the previous statement also holds (just insert another node that only forwards the words it receives from N 1 to N 1 ).…”

“…Results on NEPs, seen as generating devices, can be found, e. g., in [12,4,2,1,3]. In the seminal paper [4], it was shown that networks of evolutionary processors are universal in that sense that they can generate any recursively enumerable language, and that networks with six nodes and regular filters are sufficient to get all recursively enumerable languages; the result was further improved from the descriptional complexity point of view (see, e. g., [1]) and NEPs having only two types of nodes, and their computational power, were investigated in [2].…”

Deciding Networks of Evolutionary Processors

“…All the ANEP constructions proposed in the literature (for instance, in [10,7,1]), where one was interested only in accepting a language by complete ANEPs, can be still be used. However, we must modify such an ANEP in order to work properly in the new setting: the former output node becomes an insertion node where the symbol µ is inserted in the words that were accepted inside, and then we add a new output node, in which all the words containing µ are allowed to enter.…”

On the Power of Accepting Networks of Evolutionary Processors with Special Topologies and Random Context Filters

“…As long as nodes N (4,j) with 2 ≤ j ≤ n + 1 are entered, a further symbol Y is inserted somewhere in the word. If node N (4,1) is entered, then one Y is changed to Y ′ and the word has to move to node N (3,1) where Y ′ is replaced by X 0 . Now the word has to move to node N (2,1) where the remaining Y symbols in the word are deleted.…”

“…If node N (4,1) is entered, then one Y is changed to Y ′ and the word has to move to node N (3,1) where Y ′ is replaced by X 0 . Now the word has to move to node N (2,1) where the remaining Y symbols in the word are deleted. The obtained word z ′′ 1 X 0 z ′′ 2 satisfies z ′′ 1 z ′′ 2 = z ′ and has to enter node N (1,1) .…”