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.

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 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.

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.

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.

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.

Scattered context grammars generate any recursively enumerable language with two nonterminals

2010 ◽  
Vol 110 (20) ◽  
pp. 902-907 ◽  
Author(s):  
Erzsébet Csuhaj-Varjú ◽  
György Vaszil
Keyword(s):  
Recursively Enumerable Language ◽  
Recursively Enumerable ◽  
Enumerable Language

scholarly journals A User-Friendly Algorithm for Detecting the Influence of Background Risks on a Model

Risks ◽  
2018 ◽  
Vol 6 (3) ◽  
pp. 100 ◽  
Author(s):  
Nadezhda Gribkova ◽  
Ričardas Zitikis
Keyword(s):  
Simulated Data ◽  
Point Of View ◽  
Natural Question ◽  
Input Output ◽  
Output Data ◽  
Practical Point ◽  
Systematic Risks ◽  
User Friendly ◽  
The Given ◽  
Background Risks

Background, or systematic, risks are integral parts of many systems and models in insurance and finance. These risks can, for example, be economic in nature, or they can carry more technical connotations, such as errors or intrusions, which could be intentional or unintentional. A most natural question arises from the practical point of view: is the given system really affected by these risks? In this paper we offer an algorithm for answering this question, given input-output data and appropriately constructed statistics, which rely on the order statistics of inputs and the concomitants of outputs. Even though the idea is rooted in complex statistical and probabilistic considerations, the algorithm is easy to implement and use in practice, as illustrated using simulated data.

Principles of Modelling

1991 ◽  
Vol 24 (6) ◽  
pp. 1-8 ◽  
Author(s):  
M. B. Beck
Keyword(s):  
Model Uncertainty ◽  
Model Calibration ◽  
Field Data ◽  
Point Of View ◽  
Model Structure ◽  
Practical Point ◽  
Practical Applications ◽  
Observed Behaviour ◽  
The Given ◽  
Consistent Approach

The scope for modelling the behaviour of pollutants in the aquatic environment is now immense. In many practical applications there are effectively no computational constraints on what is possible. There is accordingly an increasing need for a set of principles of modelling that in some respects may well be different from those applicable when conceptualisation, the accuracy of the numerical solution scheme, and the inadequacies of an overly simplified model structure, were the issues of the day. Given the availability of increasingly comprehensive software, the user of a model is increasingly likely to be accelerated into a position where the issue of model calibration (identification) is an immediate problem. From the practical point of view of needing to make a decision on the control of a pollutant, the problem of identification may, or may not, be avoided. It is argued that a consistent approach to establishing whether such identification is necessary depends on establishing the significance, or otherwise, of model uncertainty. Identifying the model against field data does not have merely the goal of yielding “best” estimates of the unknown coefficients (parameters) appearing in the given model structure. It may also serve the purpose of identifying and modifying the uncertainty attaching to the model as a description of observed behaviour, which uncertainty will then be propagated forward in any predictions made with the model.

A case of congenital absence of the kidney (aplasias. agenesia renis)

1903 ◽  
Vol 3 (11-12) ◽  
pp. 586-607
Author(s):  
P. Ya. Ovchinnikov
Keyword(s):  
Point Of View ◽  
Congenital Defect ◽  
Congenital Absence ◽  
Practical Significance ◽  
Practical Point ◽  
First Case

Unilateral failure or complete absence of the kidney, which occurs in the first case as an acquired defect, in the second as a congenital defect, have significant clinical and practical significance. From a practical point of view, it seems very dangerous to have a disease of an organ in the absence of a paired one, since in this case, compensation for the defect cannot occur.

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