Countable Boolean Algebras And Decidability

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Countable Boolean Algebras And Decidability

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Author : Sergey Goncharov
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-01-31

Countable Boolean Algebras And Decidability written by Sergey Goncharov 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 1997-01-31 with Mathematics categories.

This book describes the latest Russian research covering the structure and algorithmic properties of Boolean algebras from the algebraic and model-theoretic points of view. A significantly revised version of the author's Countable Boolean Algebras (Nauka, Novosibirsk, 1989), the text presents new results as well as a selection of open questions on Boolean algebras. Other current features include discussions of the Kottonen algebras in enrichments by ideals and automorphisms, and the properties of the automorphism groups.

Decidability And Boolean Representations

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Author : Stanley Burris
language : en
Publisher: American Mathematical Soc.
Release Date : 1981

Decidability And Boolean Representations written by Stanley Burris 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 1981 with Mathematics categories.

In part I we address the question: which varieties have a decidable first order theory? We confine our attention to varieties whose algebras have modular congruence lattices (i.e., modular varieties), and focus primarily on locally finite varieties, although near the end of the paper Zamjatin's description of all decidable varieties of groups and rings, and offer a new proof of it. In part II, we show that if a variety admits such sheaf representations using only finitely many stalks, all of which are finite, then the variety can be decomposed in the product of a discriminator variety and an abelian variety. We continue this investigation by looking at well-known specializations of the sheaf construction, namely Boolean powers and sub-Boolean powers, giving special emphasis to quasi-primal algebras A, such that the sub-Boolean powers of A form a variety (this extends the work of Arens and Kaplansky on finite fields).

Programs Proofs Processes

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Author : Fernando Ferreira
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-06-17

Programs Proofs Processes written by Fernando Ferreira 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 2010-06-17 with Computers categories.

This book constitutes the refereed proceedings of the 6th Conference on Computability in Europe, CiE 2010, held in Ponta Delgada, Azores, Portugal, in June/July 2010. The 28 revised papers presented together with 20 invited lectures were carefully reviewed and selected from 90 submissions. The papers address not only the more established lines of research of computational complexity and the interplay between proofs and computation, but also novel views that rely on physical and biological processes and models to find new ways of tackling computations and improving their efficiency.

Computability And Models

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Author : Barry S. Cooper
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Computability And Models written by Barry S. Cooper 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 2012-12-06 with Mathematics categories.

Science involves descriptions of the world we live in. It also depends on nature exhibiting what we can best describe as a high aLgorithmic content. The theme running through this collection of papers is that of the interaction between descriptions, in the form of formal theories, and the algorithmic content of what is described, namely of the modeLs of those theories. This appears most explicitly here in a number of valuable, and substantial, contributions to what has until recently been known as 'recursive model theory' - an area in which researchers from the former Soviet Union (in particular Novosibirsk) have been pre-eminent. There are also articles concerned with the computability of aspects of familiar mathematical structures, and - a return to the sort of basic underlying questions considered by Alan Turing in the early days of the subject - an article giving a new perspective on computability in the real world. And, of course, there are also articles concerned with the classical theory of computability, including the first widely available survey of work on quasi-reducibility. The contributors, all internationally recognised experts in their fields, have been associated with the three-year INTAS-RFBR Research Project "Com putability and Models" (Project No. 972-139), and most have participated in one or more of the various international workshops (in Novosibirsk, Heidelberg and Almaty) and otherresearch activities of the network.

New Computational Paradigms

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Author : S.B. Cooper
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-11-28

New Computational Paradigms written by S.B. Cooper 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 2007-11-28 with Computers categories.

This superb exposition of a complex subject examines new developments in the theory and practice of computation from a mathematical perspective, with topics ranging from classical computability to complexity, from biocomputing to quantum computing. This book is suitable for researchers and graduate students in mathematics, philosophy, and computer science with a special interest in logic and foundational issues. Most useful to graduate students are the survey papers on computable analysis and biological computing. Logicians and theoretical physicists will also benefit from this book.

Automata Theory And Its Applications

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Author : Bakhadyr Khoussainov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Automata Theory And Its Applications written by Bakhadyr Khoussainov 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 2012-12-06 with Mathematics categories.

The theory of finite automata on finite stings, infinite strings, and trees has had a dis tinguished history. First, automata were introduced to represent idealized switching circuits augmented by unit delays. This was the period of Shannon, McCullouch and Pitts, and Howard Aiken, ending about 1950. Then in the 1950s there was the work of Kleene on representable events, of Myhill and Nerode on finite coset congruence relations on strings, of Rabin and Scott on power set automata. In the 1960s, there was the work of Btichi on automata on infinite strings and the second order theory of one successor, then Rabin's 1968 result on automata on infinite trees and the second order theory of two successors. The latter was a mystery until the introduction of forgetful determinacy games by Gurevich and Harrington in 1982. Each of these developments has successful and prospective applications in computer science. They should all be part of every computer scientist's toolbox. Suppose that we take a computer scientist's point of view. One can think of finite automata as the mathematical representation of programs that run us ing fixed finite resources. Then Btichi's SIS can be thought of as a theory of programs which run forever (like operating systems or banking systems) and are deterministic. Finally, Rabin's S2S is a theory of programs which run forever and are nondeterministic. Indeed many questions of verification can be decided in the decidable theories of these automata.

Model Theory And Applications

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Author : O.V. Belegradek
language : en
Publisher: American Mathematical Soc.
Release Date :

Model Theory And Applications written by O.V. Belegradek 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 with Mathematics categories.

This volume is a collection of papers on model theory and its applications. The longest paper, "Model Theory of Unitriangular Groups" by O. V. Belegradek, forms a subtle general theory behind Mal'tsev's famous correspondence between rings and groups. This is the first published paper on the topic. Given the present model-theoretic interest in algebraic groups, Belegradek's work is of particular interest to logicians and algebraists. The rest of the collection consists of papers on various questions of model theory, mainly on stability theory. Contributors are leading Russian researchers in the field.

Theory And Applications Of Models Of Computation

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Author : Xujin Chen
language : en
Publisher: Springer Nature
Release Date : 2024-05-02

Theory And Applications Of Models Of Computation written by Xujin Chen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-02 with Computers categories.

This book constitutes the proceedings of the 18th Annual Conference on Theory and Applications of Models of Computation, TAMC 2024, which was held in Hong Kong, China, during May 13–15, 2024. The 30 full papers presented in this book were carefully reviewed and selected from 69 submissions. The main themes of the selected papers are computability, complexity, algorithms, information theory, as well as their integration with machine learning theory and the foundations of artificial intelligence.

Crossroads Of Computability And Logic Insights Inspirations And Innovations

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Author : Arnold Beckmann
language : en
Publisher: Springer Nature
Release Date : 2025-06-19

Crossroads Of Computability And Logic Insights Inspirations And Innovations written by Arnold Beckmann and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-19 with Computers categories.

This book constitutes the refereed proceedings of the 21st Conference on Computability and Logic, CiE 2025, held in Lisbon, Portugal, during July 14–18, 2025. The 27 full papers included in this book were carefully reviewed and selected from 49 submissions. They focus on computability-related science, ranging over mathematics, computer science and applications in various natural and engineering sciences, such as physics and biology, as well as related fields, such as philosophy and history of computing. CiE 2025 had as its motto Crossroads of Computability and Logic: Insights, Inspirations, and Innovations, drawing on the numerous interconnections between computability research and broader logical methodologies, considering both well-established perspectives as well as recent innovations.

Unveiling Dynamics And Complexity

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Author : Jarkko Kari
language : en
Publisher: Springer
Release Date : 2017-06-07

Unveiling Dynamics And Complexity written by Jarkko Kari and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-07 with Computers categories.

This book constitutes the refereed proceedings of the 13th Conference on Computability in Europe, CiE 2017, held in Turku, Finland, in June 2017. The 24 revised full papers and 12 invited papers were carefully reviewed and selected from 69 submissions. The conference CiE 2016 has six special sessions, namly: algorithmics for biology; combinatorics and algorithmics on words; computability in analysis, algebra, and geometry; cryptography and information theory; formal languages and automata theory; and history and philosophy of computing.