Improved Descriptional Complexity Results for Simple Semi-Conditional Grammars

2021 ◽  
Vol 181 (2-3) ◽  
pp. 189-211
Author(s):  
Henning Fernau ◽  
Lakshmanan Kuppusamy ◽  
Rufus O. Oladele ◽  
Indhumathi Raman
Keyword(s):  
Normal Form ◽  
Maximum Length ◽  
Complexity Measures ◽  
Recursively Enumerable Language ◽  
Computational Completeness ◽  
Descriptional Complexity ◽  
Recursively Enumerable ◽  
Rewriting System ◽  
Complexity Results ◽  
Enumerable Language

A simple semi-conditional (SSC) grammar is a form of regulated rewriting system where the derivations are controlled either by a permitting string alone or by a forbidden string alone and this condition is specified in the rule. The maximum length i (j, resp.) of the permitting (forbidden, resp.) strings serves as a measure of descriptional complexity known as the degree of such grammars. In addition to the degree, the numbers of nonterminals and of conditional rules are also counted into the descriptional complexity measures of these grammars. We improve on some previously obtained results on the computational completeness of SSC grammars by minimizing the number of nonterminals and / or the number of conditional rules for a given degree (i, j). More specifically we prove, using a refined analysis of a normal form for type-0 grammars due to Geffert, that every recursively enumerable language is generated by an SSC grammar of (i) degree (2, 1) with eight conditional rules and nine nonterminals, (ii) degree (3, 1) with seven conditional rules and seven nonterminals (iii) degree (4, 1) with six conditional rules and seven nonterminals and (iv) degree (4, 1) with eight conditional rules and six nonterminals.

OPTIMAL RESULTS FOR THE COMPUTATIONAL COMPLETENESS OF GEMMATING (TISSUE) P SYSTEMS

2005 ◽  
Vol 16 (05) ◽  
pp. 929-942 ◽  
Author(s):  
RUDOLF FREUND ◽  
MARION OSWALD ◽  
ANDREI PĂUN
Keyword(s):  
Theoretical Model ◽  
General Model ◽  
P Systems ◽  
Optimal Result ◽  
Recursively Enumerable Language ◽  
Computational Completeness ◽  
Minimal Weight ◽  
Model Based ◽  
Recursively Enumerable ◽  
Enumerable Language

Gemmating P systems were introduced as a theoretical model based on the biological idea of the gemmation of mobile membranes. In the general model of extended gemmating P systems, strings are modified either by evolution rules in the membranes or while sending them to another membrane. We here consider the restricted variant of extended gemmating P systems with pre-dynamic rules where strings are only modified at the ends while sending them from one membrane to another one. In a series of papers the number of membranes being sufficient for obtaining computational completeness has steadily been decreased. In this paper we now prove the optimal result, i.e., gemmating P systems only using pre-dynamic rules are already computationally complete with three membranes, even in the non-extended case and with the minimal weight of rules possible. Moreover, we also show that for gemmating tissue P systems two cells suffice, and if we allow the environment to be fully involved in the communication of strings, even one cell together with the environment can manage the task to generate any recursively enumerable language.

Scattered Context Grammars with One Non-Context-Free Production are Computationally Complete

2021 ◽  
Vol 179 (4) ◽  
pp. 361-384
Author(s):  
Zbyněk Křivka ◽  
Alexander Meduna
Keyword(s):  
Open Problem ◽  
Recursively Enumerable Language ◽  
Recursively Enumerable ◽  
Enumerable Language ◽  
Context Free

This paper investigates the reduction of scattered context grammars with respect to the number of non-context-free productions. It proves that every recursively enumerable language is generated by a scattered context grammar that has no more than one non-context-free production. An open problem is formulated.

PC GRAMMAR SYSTEMS WITH CLUSTERS OF COMPONENTS

2011 ◽  
Vol 22 (01) ◽  
pp. 203-212 ◽  
Author(s):  
ERZSÉBET CSUHAJ-VARJÚ ◽  
MARION OSWALD ◽  
GYÖRGY VASZIL
Keyword(s):  
Future Research ◽  
Open Problems ◽  
Recursively Enumerable Language ◽  
Recursively Enumerable ◽  
Enumerable Language ◽  
Grammar Systems ◽  
Context Free

We introduce PC grammar systems where the components form clusters and the query symbols refer to clusters not individual grammars, i.e., the addressee of the query is not precisely identified. We prove that if the same component replies to all queries issued to a cluster in a rewriting step, then non-returning PC grammar systems with 3 clusters and 7 context-free components are able to generate any recursively enumerable language. We also provide open problems and directions for future research.

VARIANTS OF COMPETENCE-BASED DERIVATIONS IN CD GRAMMAR SYSTEMS

2010 ◽  
Vol 21 (04) ◽  
pp. 549-569 ◽  
Author(s):  
ERZSÉBET CSUHAJ-VARJÚ ◽  
JÜRGEN DASSOW ◽  
GYÖRGY VASZIL
Keyword(s):  
Recursively Enumerable Language ◽  
Recursively Enumerable ◽  
Enumerable Language ◽  
Sentential Form ◽  
Grammar Systems ◽  
The Given

In this paper we introduce and study some new cooperation protocols for cooperating distributed (CD) grammar systems. These derivation modes depend on the number of different nonterminals present in the sentential form obtained when a component finished a derivation phase. This measure describes the competence of the grammar on the string (the competence is high if the number of the different nonterminals is small). It is also a measure of the efficiency of the grammar on the given string (a component is more efficient than another one if it is able to decrease the number of nonterminals in the string to a greater extent). We prove that if the underlying derivation mode is the t-mode derivation, then some variants of these systems determine the class of random context ET0L languages. If these CD grammar systems use the k step limited derivations as underlying derivation mode, then they are able to generate any recursively enumerable language.

On the size complexity of universal accepting hybrid networks of evolutionary processors

2007 ◽  
Vol 17 (4) ◽  
pp. 753-771 ◽  
Author(s):  
FLORIN MANEA ◽  
CARLOS MARTIN-VIDE ◽  
VICTOR MITRANA
Keyword(s):  
Point Of View ◽  
Hybrid Networks ◽  
Underlying Structure ◽  
Recursively Enumerable Language ◽  
Practical Point ◽  
Computing Model ◽  
Recursively Enumerable ◽  
First Case ◽  
Enumerable Language ◽  
The Given

In this paper we discuss the following interesting question about accepting hybrid networks of evolutionary processors (AHNEP), which are a recently introduced bio-inspired computing model. The question is: how many processors are required in such a network to recognise a given language L? Two answers are proposed for the most general case, when L is a recursively enumerable language, and both answers improve on the previously known bounds. In the first case the network has a number of processors that is linearly bounded by the cardinality of the tape alphabet of a Turing machine recognising the given language L. In the second case we show that an AHNEP with a fixed underlying structure can accept any recursively enumerable language. The second construction has another useful property from a practical point of view as it includes a universal AHNEP as a subnetwork, and hence only a limited number of its parameters depend on the given language.

ON THE DESCRIPTIONAL COMPLEXITY OF ACCEPTING NETWORKS OF EVOLUTIONARY PROCESSORS WITH FILTERED CONNECTIONS

2008 ◽  
Vol 19 (05) ◽  
pp. 1113-1132 ◽  
Author(s):  
CEZARA DRĂGOI ◽  
FLORIN MANEA
Keyword(s):  
Point Of View ◽  
The Other ◽  
Input Word ◽  
Output Node ◽  
Descriptional Complexity ◽  
Recursively Enumerable ◽  
Enumerable Language ◽  
Network Of Evolutionary Processors ◽  
Nondeterministic Turing Machine ◽  
The Given

In this paper we consider, from the descriptional complexity point of view, a model of computation introduced in [1], namely accepting network of evolutionary processors with filtered connections (ANEPFCs). First we show that for each morphism h : V → W*, with V ∩ W = ∅, one can effectively construct an ANEPFC, of size 6 + |W|, which accepts every input word w and, at the end of the computation on this word, obtains h(w) in its output node. This result can be applied in constructing two different ANEPFCs, with 27 and, respectively, 26 processors, recognizing a given recursively enumerable language. The first architecture, based on the construction of a universal ANEPFC, has the property that only 7 of its 27 processors depend on the accepted language. On the other hand, all the 26 processors of the second architecture depend on the accepted language, but, differently from the first one, this network simulates efficiently (from both time and space perspectives) a nondeterministic Turing machine accepting the given language.

scholarly journals GENERATING ALL CIRCULAR SHIFTS BY CONTEXT-FREE GRAMMARS IN GREIBACH NORMAL FORM

2007 ◽  
Vol 18 (06) ◽  
pp. 1139-1149 ◽  
Author(s):  
PETER R. J. ASVELD
Keyword(s):  
Normal Form ◽  
Complexity Measures ◽  
Descriptional Complexity ◽  
Low Degree ◽  
Cyclic Shifts ◽  
Low Degree Polynomials ◽  
Context Free ◽  
Greibach Normal Form ◽  
Context Free Grammars

For each alphabet Σn = {a1,a2,…,an}, linearly ordered by a1 < a2 < ⋯ < an, let Cn be the language of circular or cyclic shifts over Σn, i.e., Cn = {a1a2 ⋯ an-1an, a2a3 ⋯ ana1,…,ana1 ⋯ an-2an-1}. We study a few families of context-free grammars Gn (n ≥1) in Greibach normal form such that Gn generates Cn. The members of these grammar families are investigated with respect to the following descriptional complexity measures: the number of nonterminals ν(n), the number of rules π(n) and the number of leftmost derivations δ(n) of Gn. As in the case of Chomsky normal form, these ν, π and δ are functions bounded by low-degree polynomials. However, the question whether there exists a family of grammars that is minimal w. r. t. all these measures remains open.

DYNAMICALLY FORMED CLUSTERS OF AGENTS IN ECO-GRAMMAR SYSTEMS

2009 ◽  
Vol 20 (02) ◽  
pp. 293-311 ◽  
Author(s):  
KATALIN ANNA LÁZÁR ◽  
ERZSÉBET CSUHAJ-VARJÚ ◽  
ANDRÁS LŐRINCZ ◽  
GYÖRGY VASZIL
Keyword(s):  
Regular Language ◽  
Clustering Algorithm ◽  
Research Directions ◽  
Recursively Enumerable Language ◽  
Chomsky Hierarchy ◽  
Recursively Enumerable ◽  
Enumerable Language ◽  
Language Classes ◽  
L Systems ◽  
Grammar Systems

In this paper we extend the conditions of dynamic team constitution in simple eco–grammar systems, motivated by the bottom–up–clustering algorithm. The relationships of simple eco–grammar systems formed according to the newly introduced conditions to each other as well as to certain language classes of the Chomsky hierarchy and L systems are established. We prove that any recursively enumerable language can be obtained as the intersection of a regular language and the language of simple eco–grammar systems where the active teams are organized according to different conditions of team constitution. We also propose some further research directions.

scholarly journals On the Power of Small Size Insertion P Systems

2011 ◽  
Vol 6 (2) ◽  
pp. 266 ◽  
Author(s):  
Alexander Krassovitskiy
Keyword(s):  
P Systems ◽  
Computational Power ◽  
Recursively Enumerable Language ◽  
Recursively Enumerable ◽  
Enumerable Language ◽  
The Family ◽  
Context Free

In this article we investigate insertion systems of small size in the framework of P systems. We consider P systems with insertion rules having one symbol context and we show that they have the computational power of context-free matrix grammars. If contexts of length two are permitted, then any recursively enumerable language can be generated. In both cases a squeezing mechanism, an inverse morphism, and a weak coding are applied to the output of the corresponding P systems. We also show that if no membranes are used then corresponding family is equal to the family of context-free languages.

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