scholarly journals Fixed Points Results in Algebras of Split Quaternion and Octonion

Symmetry ◽  
2018 ◽  
Vol 10 (9) ◽  
pp. 405 ◽  
Author(s):  
Mobeen Munir ◽  
Asim Naseem ◽  
Akhtar Rasool ◽  
Muhammad Saleem ◽  
Shin Kang
Keyword(s):  
Game Theory ◽  
Computer Science ◽  
Fixed Points ◽  
Quadratic Polynomial ◽  
Split Quaternion ◽  
Finite Algebras ◽  
Prime Fields

Fixed points of functions have applications in game theory, mathematics, physics, economics and computer science. The purpose of this article is to compute fixed points of a general quadratic polynomial in finite algebras of split quaternion and octonion over prime fields Z p. Some characterizations of fixed points in terms of the coefficients of these polynomials are also given. Particularly, cardinalities of these fixed points have been determined depending upon the characteristics of the underlying field.

scholarly journals Some Fixed Points Results of Quadratic Functions in Split Quaternions

2016 ◽  
Vol 2016 ◽  
pp. 1-5 ◽  
Author(s):  
Young Chel Kwun ◽  
Mobeen Munir ◽  
Waqas Nazeer ◽  
Shin Min Kang
Keyword(s):  
Fixed Points ◽  
Quadratic Polynomial ◽  
Quadratic Functions ◽  
Split Quaternion ◽  
Quadratic Polynomials ◽  
Split Quaternions

We attempt to find fixed points of a general quadratic polynomial in the algebra of split quaternion. In some cases, we characterize fixed points in terms of the coefficients of these polynomials and also give the cardinality of these points. As a consequence, we give some simple examples to strengthen the infinitude of these points in these cases. We also find the roots of quadratic polynomials as simple consequences.

Noncooperative Game Theory

2017 ◽  
Author(s):  
João P. Hespanha
Keyword(s):  
Game Theory ◽  
Computer Science ◽  
Dynamic Games ◽  
Design Methodology ◽  
Noncooperative Game ◽  
Noncooperative Game Theory ◽  
Original Design ◽  
Theoretical Perspectives ◽  
Engineering Designs ◽  
Zero Sum

This book is aimed at students interested in using game theory as a design methodology for solving problems in engineering and computer science. The book shows that such design challenges can be analyzed through game theoretical perspectives that help to pinpoint each problem's essence: Who are the players? What are their goals? Will the solution to “the game” solve the original design problem? Using the fundamentals of game theory, the book explores these issues and more. The use of game theory in technology design is a recent development arising from the intrinsic limitations of classical optimization-based designs. In optimization, one attempts to find values for parameters that minimize suitably defined criteria—such as monetary cost, energy consumption, or heat generated. However, in most engineering applications, there is always some uncertainty as to how the selected parameters will affect the final objective. Through a sequential and easy-to-understand discussion, the book examines how to make sure that the selection leads to acceptable performance, even in the presence of uncertainty—the unforgiving variable that can wreck engineering designs. The book looks at such standard topics as zero-sum, non-zero-sum, and dynamic games and includes a MATLAB guide to coding. This book offers students a fresh way of approaching engineering and computer science applications.

Computer science and game theory

2008 ◽  
Vol 51 (8) ◽  
pp. 74-79 ◽  
Author(s):  
Yoav Shoham
Keyword(s):  
Game Theory ◽  
Computer Science

scholarly journals Fuzzy fixed points of generalized F2-Geraghty type fuzzy mappings and complementary results

2016 ◽  
Vol 21 (2) ◽  
pp. 274-292 ◽  
Author(s):  
Mujahid Abbas ◽  
Basit Ali ◽  
Ornella Rizzo ◽  
Calogero Vetro
Keyword(s):  
Fixed Point ◽  
Computer Science ◽  
Fixed Points ◽  
Metric Space ◽  
Type Theorem ◽  
Theoretical Computer Science ◽  
Theoretical Computer ◽  
Hybrid Pair ◽  
Fuzzy Fixed Point

The aim of this paper is to introduce generalized F2-Geraghty type fuzzy mappings on a metric space for establishing the existence of fuzzy fixed points of such mappings. As an application of our result, we obtain the existence of common fuzzy fixed point for a generalized F2-Geraghty type fuzzy hybrid pair. These results unify, generalize and complement various known comparable results in the literature. An example and an application to theoretical computer science are presented to support the theory proved herein. Also, to suggest further research on fuzzy mappings, a Feng–Liu type theorem is proved.

Introduction

2014 ◽  
pp. 1-20
Keyword(s):  
Game Theory ◽  
Computer Science ◽  
Planning Under Uncertainty ◽  
Problems And Solutions ◽  
The Status ◽  
The Game Theory ◽  
Close Study ◽  
Competitive Nature ◽  
Area Of Application

The situations to which game theory has actually been applied reflect its selective usefulness for problems and solutions of an individualistic and competitive nature, building in the values of the status quo. The main principal area of application has been economics. In economics, game theory has been used in studying competition for markets, advertising, planning under uncertainty, and so forth. Recently, game theory has also been applied to many other fields, such as law, ethics, sociology, biology, and of course, computer science. In all these applications, a close study of the formulation of the problem in the game theory perspective shows a strong inclination to work from existing values, to consider only currently contending parties and options, and in other ways, to exclude significant redefinitions of the problems at hand. This introductory chapter explores these and forms a basis for the rest of the book.

scholarly journals Reports of the AAAI 2012 Spring Symposia

AI Magazine ◽  
2012 ◽  
Vol 33 (3) ◽  
pp. 109
Author(s):  
Harith Alani ◽  
Bo An ◽  
Manish Jain ◽  
Takashi Kido ◽  
George Konidaris ◽  
...  
Keyword(s):  
Artificial Intelligence ◽  
Game Theory ◽  
Computer Science ◽  
Social Computing ◽  
Collective Intelligence ◽  
Intelligent Robots ◽  
Personal Wellness ◽  
Technical Report Series ◽  
Symposium Series ◽  
Technical Report

The Association for the Advancement of Artificial Intelligence, in cooperation with Stanford University’s Department of Computer Science, was pleased to present the 2012 Spring Symposium Series, held Monday through Wednesday, March 26–28, 2012 at Stanford University, Stanford, California USA. The six symposia held were AI, The Fundamental Social Aggregation Challenge (cochaired by W. F. Lawless, Don Sofge, Mark Klein, and Laurent Chaudron); Designing Intelligent Robots (cochaired by George Konidaris, Byron Boots, Stephen Hart, Todd Hester, Sarah Osentoski, and David Wingate); Game Theory for Security, Sustainability, and Health (cochaired by Bo An and Manish Jain); Intelligent Web Services Meet Social Computing (cochaired by Tomas Vitvar, Harith Alani, and David Martin); Self-Tracking and Collective Intelligence for Personal Wellness (cochaired by Takashi Kido and Keiki Takadama); and Wisdom of the Crowd (cochaired by Caroline Pantofaru, Sonia Chernova, and Alex Sorokin). The papers of the six symposia were published in the AAAI technical report series.

Weak Separation Problem for Tree Languages

2020 ◽  
Vol 31 (05) ◽  
pp. 583-593
Author(s):  
Saeid Alirezazadeh ◽  
Khadijeh Alibabaei
Keyword(s):  
Computer Science ◽  
Natural Extension ◽  
Classical Problem ◽  
Finite Alphabet ◽  
Direct Products ◽  
Separation Problem ◽  
Finite Algebras ◽  
Tree Languages ◽  
Weak Separation ◽  
Recognizable Language

Forest algebras are defined for investigating languages of forests [ordered sequences] of unranked trees, where a node may have more than two [ordered] successors. They consist of two monoids, the horizontal and the vertical, with an action of the vertical monoid on the horizontal monoid, and a complementary axiom of faithfulness. A pseudovariety is a class of finite algebras of a given signature, closed under the taking of homomorphic images, subalgebras and finitary direct products. By looking at the syntactic congruence for monoids and as the natural extension in the case of forest algebras, we could define a version of syntactic congruence of a subset of the free forest algebra, not just a forest language. Let [Formula: see text] be a finite alphabet and [Formula: see text] be a pseudovariety of finite forest algebras. A language [Formula: see text] is [Formula: see text]-recognizable if its syntactic forest algebra belongs to [Formula: see text]. Separation is a classical problem in mathematics and computer science. It asks whether, given two sets belonging to some class, it is possible to separate them by another set of a smaller class. Suppose that a forest language [Formula: see text] and a forest [Formula: see text] are given. We want to find if there exists any proof for that [Formula: see text] does not belong to [Formula: see text] just by using [Formula: see text]-recognizable languages, i.e. given such [Formula: see text] and [Formula: see text], if there exists a [Formula: see text]-recognizable language [Formula: see text] which contains [Formula: see text] and does not contain [Formula: see text]. In this paper, we present how one can use profinite forest algebra to separate a forest language and a forest term and also to separate two forest languages.

scholarly journals Exploiting Game Theory for Analysing Justifications

2020 ◽  
Vol 20 (6) ◽  
pp. 880-894
Author(s):  
SIMON MARYNISSEN ◽  
BART BOGAERTS ◽  
MARC DENECKER
Keyword(s):  
Game Theory ◽  
Logic Programming ◽  
Computer Science ◽  
Central Concept ◽  
Semantic Framework ◽  
The Third ◽  
The Past ◽  
Theoretical Foundations

AbstractJustification theory is a unifying semantic framework. While it has its roots in non-monotonic logics, it can be applied to various areas in computer science, especially in explainable reasoning; its most central concept is a justification: an explanation why a property holds (or does not hold) in a model.In this paper, we continue the study of justification theory by means of three major contributions. The first is studying the relation between justification theory and game theory. We show that justification frameworks can be seen as a special type of games. The established connection provides the theoretical foundations for our next two contributions. The second contribution is studying under which condition two different dialects of justification theory (graphs as explanations vs trees as explanations) coincide. The third contribution is establishing a precise criterion of when a semantics induced by justification theory yields consistent results. In the past proving that such semantics were consistent took cumbersome and elaborate proofs.We show that these criteria are indeed satisfied for all common semantics of logic programming.

Playing with Ambiguity

Game Theory ◽  
2017 ◽  
pp. 52-70
Author(s):  
Konstantinos Georgalos
Keyword(s):  
Game Theory ◽  
Computer Science ◽  
Reliable Data ◽  
Simulation Methods ◽  
Agent Based Simulation ◽  
Economic Experiments ◽  
Agent Based ◽  
Stag Hunt Game ◽  
Beliefs And Attitudes ◽  
Design Experiments

This chapter discusses the way that three distinct fields, decision theory, game theory and computer science, can be successfully combined in order to optimally design economic experiments. Using an example of cooperative game theory (the Stag-Hunt game), the chapter presents how the introduction of ambiguous beliefs and attitudes towards ambiguity in the analysis can affect the predicted equilibrium. Based on agent-based simulation methods, the author is able to tackle similar theoretical problems and thus to design experiments in such a way that they will produce useful, unbiased and reliable data.

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