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Hyperidentities And Clones

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Hyperidentities And Clones

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Author : Klaus Denecke
language : en
Publisher: CRC Press
Release Date : 2000-08-08

Hyperidentities And Clones written by Klaus Denecke and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-08-08 with Mathematics categories.

Theories and results on hyperidentities have been published in various areas of the literature over the last 18 years. Hyperidentities and Clones integrates these into a coherent framework for the first time. The author also includes some applications of hyperidentities to the functional completeness problem in multiple-valued logic and extends the

Hyperidentities Boolean And De Morgan Structures

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Author : Yuri Movsisyan
language : en
Publisher: World Scientific
Release Date : 2022-09-20

Hyperidentities Boolean And De Morgan Structures written by Yuri Movsisyan and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-20 with Mathematics categories.

Hyperidentities are important formulae of second-order logic, and research in hyperidentities paves way for the study of second-order logic and second-order model theory.This book illustrates many important current trends and perspectives for the field of hyperidentities and their applications, of interest to researchers in modern algebra and discrete mathematics. It covers a number of directions, including the characterizations of the Boolean algebra of n-ary Boolean functions and the distributive lattice of n-ary monotone Boolean functions; the classification of hyperidentities of the variety of lattices, the variety of distributive (modular) lattices, the variety of Boolean algebras, and the variety of De Morgan algebras; the characterization of algebras with aforementioned hyperidentities; the functional representations of finitely-generated free algebras of various varieties of lattices and bilattices via generalized Boolean functions (De Morgan functions, quasi-De Morgan functions, super-Boolean functions, super-De Morgan functions, etc); the structural results for De Morgan algebras, Boole-De Morgan algebras, super-Boolean algebras, bilattices, among others.While problems of Boolean functions theory are well known, the present book offers alternative, more general problems, involving the concepts of De Morgan functions, quasi-De Morgan functions, super-Boolean functions, and super-De Morgan functions, etc. In contrast to other generalized Boolean functions discovered and investigated so far, these functions have clearly normal forms. This quality is of crucial importance for their applications in pure and applied mathematics, especially in discrete mathematics, quantum computation, quantum information theory, quantum logic, and the theory of quantum computers.

Algebras And Orders

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Author : Ivo G. Rosenberg
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Algebras And Orders written by Ivo G. Rosenberg and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.

In the summer of 1991 the Department of Mathematics and Statistics of the Universite de Montreal was fortunate to host the NATO Advanced Study Institute "Algebras and Orders" as its 30th Seminaire de mathematiques superieures (SMS), a summer school with a long tradition and well-established reputation. This book contains the contributions of the invited speakers. Universal algebra- which established itself only in the 1930's- grew from traditional algebra (e.g., groups, modules, rings and lattices) and logic (e.g., propositional calculus, model theory and the theory of relations). It started by extending results from these fields but by now it is a well-established and dynamic discipline in its own right. One of the objectives of the ASI was to cover a broad spectrum of topics in this field, and to put in evidence the natural links to, and interactions with, boolean algebra, lattice theory, topology, graphs, relations, automata, theoretical computer science and (partial) orders. The theory of orders is a relatively young and vigorous discipline sharing certain topics as well as many researchers and meetings with universal algebra and lattice theory. W. Taylor surveyed the abstract clone theory which formalizes the process of compos ing operations (i.e., the formation of term operations) of an algebra as a special category with countably many objects, and leading naturally to the interpretation and equivalence of varieties.

Advances In Algebra And Combinatorics Proceedings Of The Second International Congress In Algebra And Combinatorics

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Author : K. P. Shum
language : en
Publisher: World Scientific
Release Date : 2008

Advances In Algebra And Combinatorics Proceedings Of The Second International Congress In Algebra And Combinatorics written by K. P. Shum and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.

This volume is a compilation of lectures on algebras and combinatorics presented at the Second International Congress in Algebra and Combinatorics. It reports on not only new results, but also on open problems in the field. The proceedings volume is useful for graduate students and researchers in algebras and combinatorics. Contributors include eminent figures such as V Artamanov, L Bokut, J Fountain, P Hilton, M Jambu, P Kolesnikov, Li Wei and K Ueno.

Advances In Algebra And Combinatorics Proceedings Of The Second International Congress In Algebra And Combinatorics

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Author : Kar Ping Shum
language : en
Publisher: World Scientific
Release Date : 2008-06-17

Advances In Algebra And Combinatorics Proceedings Of The Second International Congress In Algebra And Combinatorics written by Kar Ping Shum and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-06-17 with Mathematics categories.

Proceedings Of The International Conference On Algebra Dedicated To The Memory Of A I Mal Cev

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Author : Leonid A. Bokut'
language : en
Publisher: American Mathematical Soc.
Release Date : 1992

Proceedings Of The International Conference On Algebra Dedicated To The Memory Of A I Mal Cev written by Leonid A. Bokut' and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Algebra categories.

Universal Algebra And Coalgebra

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Author : Klaus Denecke
language : en
Publisher: World Scientific
Release Date : 2009

Universal Algebra And Coalgebra written by Klaus Denecke and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.

The purpose of this book is to study the structures needed to model objects in universal algebra, universal coalgebra and theoretical computer science. Universal algebra is used to describe different kinds of algebraic structures, while coalgebras are used to model state-based machines in computer science.The connection between algebras and coalgebras provides a way to connect static data-oriented systems with dynamical behavior-oriented systems. Algebras are used to describe data types and coalgebras describe abstract systems or machines.The book presents a clear overview of the area, from which further study may proceed.

Proceedings Of The International Conference On Semigroups

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Author : Paula Smith
language : en
Publisher: World Scientific
Release Date : 2000

Proceedings Of The International Conference On Semigroups written by Paula Smith and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.

This book contains contributions by leading experts which cover an extensive range of topics in semigroups theory. Some of the articles exhibit the strong links with theoretical computer science. Several survey articles summarize the salient features of special fields of the theory of particular interest in the contemporary research. Special care has been taken in the presentation of the papers, making them accessible to a large audience.

Function Algebras On Finite Sets

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Author : Dietlinde Lau
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-11-23

Function Algebras On Finite Sets written by Dietlinde Lau and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-23 with Mathematics categories.

Functions which are defined on finite sets occur in almost all fields of mathematics. For more than 80 years algebras whose universes are such functions (so-called function algebras), have been intensively studied. This book gives a broad introduction to the theory of function algebras and leads to the cutting edge of research. To familiarize the reader from the very beginning on with the algebraic side of function algebras the more general concepts of the Universal Algebra is given in the first part of the book. The second part on fuction algebras covers the following topics: Galois-connection between function algebras and relation algebras, completeness criterions, clone theory. This book is an insdispensible source on function algebras for graduate students and researchers in mathematical logic and theoretical computer science.

Universal Algebra And Applications In Theoretical Computer Science

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Author : Klaus Denecke
language : en
Publisher: CRC Press
Release Date : 2018-10-03

Universal Algebra And Applications In Theoretical Computer Science written by Klaus Denecke and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-03 with Mathematics categories.

Over the past 20 years, the emergence of clone theory, hyperequational theory, commutator theory and tame congruence theory has led to a growth of universal algebra both in richness and in applications, especially in computer science. Yet most of the classic books on the subject are long out of print and, to date, no other book has integrated these theories with the long-established work that supports them. Universal Algebra and Applications in Theoretical Computer Science introduces the basic concepts of universal algebra and surveys some of the newer developments in the field. The first half of the book provides a solid grounding in the core material. A leisurely pace, careful exposition, numerous examples, and exercises combine to form an introduction to the subject ideal for beginning graduate students or researchers from other areas. The second half of the book focuses on applications in theoretical computer science and advanced topics, including Mal'cev conditions, tame congruence theory, clones, and commutators. The impact of the advances in universal algebra on computer science is just beginning to be realized, and the field will undoubtedly continue to grow and mature. Universal Algebra and Applications in Theoretical Computer Science forms an outstanding text and offers a unique opportunity to build the foundation needed for further developments in its theory and in its computer science applications.

Hyperidentities And Clones

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