Accepting Networks of Evolutionary Processors with Subregular Filters

RAIRO-Theor. Inf. Appl.

Truthe

2021

Self Cite

In this paper, we continue the research on accepting networks of evolutionary processors where the filters belong to several special families of regular languages. We consider families of codes or ideals and subregular families which are defined by restricting the resources needed for generating or accepting them (the number of states of the minimal deterministic finite automaton accepting a language of the family as well as the number of non-terminal symbols or the number of production rules of a right-linear grammar generating such a language). We insert the newly defined language families into the hierachy of language families obtained by using as filters languages of other subregular families (such as ordered, non-counting, power-separating, circular, suffix-closed regular, union-free, definite, combinational, finite, monoidal, nilpotent, or commutative languages).

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Accepting networks of evolutionary processors with resources restricted and structure limited filters

RAIRO-Theor. Inf. Appl.

Truthe

2021

Self Cite

“…The computational complexity of ANEPs with restrictions regarding the rules or with other types of filters (filters taken from other subclasses of the class of regular languages) was investigated, for instance, in [6] and [11], respectively. In [5], the computational and descriptional complexity of ANEPs with a special shape (star, wheel, grid) was studied.…”

Section: Introductionmentioning

confidence: 99%

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

Fundamenta Informaticae

Manea

Truthe

2015

Self Cite

In this paper, we approach the problem of accepting all recursively enumerable languages by accepting networks of evolutionary processors (ANEPs, for short) with a fixed architecture. More precisely, we show that every recursively enumerable language can be accepted by an ANEP with an underlying graph in the form of a star with 13 nodes or by an ANEP with an underlying grid with 13 × 4 = 52 nodes as well as by ANEPs having underlying graphs in the form of a chain, a ring, or a wheel with 29 nodes each. In all these cases, the size and form as well as the general working strategy of the constructed networks do not depend on the accepted language; only the rewriting rules and the filters associated to each node of the networks depend on this language. Noteworthy is also the fact that the filtering process is implemented using random context conditions only. Our results answer problems which were left open in a paper published by J. Dassow and F. Manea at the conference on Descriptional Complexity of Formal Systems (DCFS) 2010 and improve a result published by B. Truthe at the conference on Non-Classical Models of Automata and Applications (NCMA) 2013. This paper is an extended version of the contributions to the conferences DCFS 2010 ([5]) and NCMA 2013 ([17]). ‡ The work of Florin Manea was supported by the DFG grant 596676. § The results were obtained while Bianca Truthe worked at the Otto-von-Guericke-Universität Magdeburg, Germany. J. Dassow et al. / On the Power of ANEPs with Special Topologies and RC Filters 3 DefinitionsWe assume that the reader is familiar with the basic concepts of formal language theory (see e. g. [16]). We only recall here some notations used in the paper.An alphabet is a finite and nonempty set of symbols. The set of all words over V is denoted by V * and the empty word is denoted by λ. The length of a word x is denoted by |x| while alph(x) denotes the minimal alphabet W such that x ∈ W * . For a word x ∈ W * , we denote by x r the reversal of the word.We denote by ⊆ the inclusion relation of sets and by ⊂ the relation of strict inclusion. A phrase structure grammar is specified as a quadruple G = (N, T, P, S)where N and T are alphabets (the elements of N are called non-terminal symbols; the elements of T are called terminal symbols), P is a finite set of production rules which are written in the form

“…Since on the one hand practical requirement do not ask for arbitrary regular languages and on the other hand theoretical studies -for instance proofs -show that only special regular languages are used, it is very natural to study the devices with subregular languages for the control. Investigations on the change of the generative power, if subregular restrictions defined by combinatorial and algebraic properties are done in [4] for regularly controlled grammars, in [8,10] for conditional grammars, in [16] for tree controlled grammars, in [11,25] for networks with evolutionary processors, and in [7,12] for contextual grammars. Results on the effect of subregular restrictions given by bounds on the number of states/nonterminals/productions necessary to accept/generate the regular language can be found in [6] for regularly controlled grammars, in [5] for conditional grammars, in [15] for tree controlled grammars, in [17] for networks with evolutionary processors, and in [12,26] for contextual grammars.…”

Section: Introductionmentioning

confidence: 99%

Conditional Lindenmayer systems with subregular conditions: The non-extended case

RAIRO-Theor. Inf. Appl.

Rudolf²

2014

We consider conditional tabled Lindenmayer sytems without interaction, where each table is associated with a regular set and a table can only be applied to a sentential form which is contained in its associated regular set. We study the effect to the generative power, if we use instead of arbitrary regular languages only finite, nilpotent, monoidal, combinational, definite, ordered, union-free, star-free, strictly locally testable, commutative regular, circular regular, and suffix-closed regular languages. Essentially, we prove that the hierarchy of language families obtained from conditional Lindenmayer systems with subregular conditions is almost identical to the hierarchy of families of subregular languages.