Sherzod Turaev

Software Quality Models: A Comparative Study

In last decade, researchers have often tried to improve the usability, portability, integrity and other aspects of software in order for it to be more users friendly and gain user trust. Several approaches and techniques have been proposed to reduce the negative effects of software size and complexity. Moreover, several software quality models were proposed to evaluate general and specific type of software products. These models were proposed to evaluate general or specific scopes of software products. The proposed models were developed based on comparisons between the well-known models, in order to customize the closed model to the intended scope. These comparisons are leak of criteria that is conducted based on different perspectives and understanding. Therefore, a formal method of comparison between software quality models is proposed. The proposed method is applied on a comprehensive comparison between well-known software quality models. The result of the proposed method shows the strength and weaknesses of those models.

k-Petri Net Controlled Grammars

We introduce a new type of regulated grammars using Petri nets as a control of the derivations of a context-free grammar. We investigate the generative power and give closure properties of the families of languages generated by such Petri net controlled grammars.

Grammars Controlled by Special Petri Nets

A Petri net controlled grammar is a context-free grammar with a control by a Petri net whose transitions are labeled with rules of the grammar or the empty string and the associated language consists of all terminal strings which can be derived in the grammar and the sequence of rules in a derivation is in the image of a successful occurrence of transitions of the net. We present some results on the generative capacities of such grammars that Petri nets are restricted to some known structural subclasses of Petri nets.

Nonterminal complexity of tree controlled grammars

This paper studies the nonterminal complexity of tree controlled grammars. It is proved that the number of nonterminals in tree controlled grammars without erasing rules leads to an infinite hierarchy of families of tree controlled languages, while every recursively enumerable language can be generated by a tree controlled grammar with erasing rules and at most nine nonterminals.

Consensus of fractional nonlinear dynamics stochastic operators for multi-agent systems

Abstract In this paper, we consider nonlinear models of DeGroot, quadratic stochastic operators (QSO) and doubly stochastic quadratic operators (DSQO) with fractional degree for consensus problem in multi-agent systems (MAS). By the limit behaviour of nonlinear approach, we discuss the convergence of the solutions of the models considered. The findings from the results of the carried out investigation demonstrates an efficient approach to convergence for consensus problem in MAS. The main advantages of the proposed work are i) fast convergence to consensus ii) flexible and low complexity in computation iii) ability to achieve optimal consensus. The study is built on fractional representation of 1 n where n → ∞. Further, the simulation results on the related protocols are also presented.

Dynamics of doubly stochastic quadratic operators on a finite-dimensional simplex

Abstract The present paper focuses on the dynamics of doubly stochastic quadratic operators (d.s.q.o) on a finite-dimensional simplex. We prove that if a d.s.q.o. has no periodic points then the trajectory of any initial point inside the simplex is convergent. We show that if d.s.q.o. is not a permutation then it has no periodic points on the interior of the two dimensional (2D) simplex. We also show that this property fails in higher dimensions. In addition, the paper also discusses the dynamics classifications of extreme points of d.s.q.o. on two dimensional simplex. As such, we provide some examples of d.s.q.o. which has a property that the trajectory of any initial point tends to the center of the simplex. We also provide and example of d.s.q.o. that has infinitely many fixed points and has infinitely many invariant curves. We therefore came-up with a number of evidences. Finally, we classify the dynamics of extreme points of d.s.q.o. on 2D simplex.

Reach a nonlinear consensus for MAS via doubly stochastic quadratic operators

ABSTRACT This technical note addresses the new nonlinear protocol class of doubly stochastic quadratic operators (DSQOs) for coordination of consensus problem in multi-agent systems (MAS). We derive the conditions for ensuring that every agent reaches consensus on a desired rate of the groups decision where the group decision value in its agents initial statuses varies. Besides that, we investigate a nonlinear protocol sub-class of extreme DSQO (EDSQO) to reach a consensus for MAS to a common value with nonlinear low-complexity rules and fast time convergence if the interactions for each agent are not selfish. In addition, to extend the results to reach a consensus and to avoid the selfish case we specify a general class of DSQO for reaching a consensus under any given case of initial states. The case that MAS reach a consensus by DSQO is if each member of the agent group has positive interactions of DSQO (PDSQO) with the others. The convergence of both EDSQO and PDSQO classes is found to be directed towards the centre point. Finally, experimental simulations are given to support the analysis from theoretical aspect.

Dynamics classifications of extreme doubly stochastic quadratic operators on 2D simplex

We study the dynamics of extreme doubly stochastic quadratic operators (d.s.q.o.) on two dimensional (2D) simplex. We provide some examples of d.s.q.o. which have infinitely many fixed points. We prove that the trajectory of extreme d.s.q.o., starting at some interior point of the simplex is convergent. Finally, we classify the dynamics of all extreme points of d.s.q.o. on 2D.

The Extreme Doubly Stochastic Quadratic Operators on Two Dimensional Simplex

Multi agent systems and consensus problems are theoretical aspect of Quadratic Stochastic Operators (QSO). The extreme doubly stochastic quadratic operators (EDSQOs) on two-dimensional simplex (2DS) exposes a complex problem within QSO and majorization theories in non-linear model. Previous research studies on EDSQOs fails to present full transition matrices and operators of EDSQOs on 2DS. Crucial to that is the classification of those operators within each permutation. In order to address these gaps, this research designed all the transition matrices for each EDSQO on 2DS under the sufficient conditions of majorization concept. Hence, the study defines all the EDSQOs on 2DS and investigate the sufficient conditions of Majorization concept for EDSQOs on 2DS. Matlab is utilize for analysis of evaluating the number of EDSQOs on 2DS. The result of the analysis of the transition matrices and operators indicates 222 EDSQOs on 2DS. Further analysis enables this research to classify the 222 EDSQOs into 37 groups of EDSQOs based on a permutation of each EDSQOs. This study has impact on a model for consensus problems and multi agent systems.

Grammars controlled by Petri Nets

Formal language theory, introduced by Noam Chomsky in the 1950s as a tool for a description of natural languages [8–10], has also been widely involved in modeling and investigating phenomena appearing in computer science, artificial intelligence and other related fields because the symbolic representation of a modeled system in the form of strings makes its processes by information processing tools very easy: coding theory, cryptography, computation theory, computational linguistics, natural computing, and many other fields directly use sets of strings for the description and analysis of modeled systems. In formal language theory a model for a phenomenon is usually constructed by representing it as a set of words, i.e., a language over a certain alphabet, and defining a generative mechanism, i.e., a grammar which identifies exactly the words of this set. With respect to the forms of their rules, grammars and their languages are divided into four classes of Chomsky hierarchy: recursively enumerable, context-sensitive, context-free and regular.