Download or read book Complexity and Randomness in Group Theory written by Frédérique Bassino and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-06-08 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: Detailed Description

Download or read book Groups and Model Theory written by Olga Kharlampovich and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-05-10 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides an overview of developments in group theory motivated by model theory by key international researchers in the field. Topics covered include: stable groups and generalizations, model theory of nonabelian free groups and of rigid solvable groups, pseudofinite groups, approximate groups, topological dynamics, groups interpreting the arithmetic. The book is intended for mathematicians and graduate students in group theory and model theory. The book follows the course of the GAGTA (Geometric and Asymptotic Group Theory with Applications) conference series. The first book, "Complexity and Randomness in Group Theory. GAGTA book 1," can be found here: http://www.degruyter.com/books/978-3-11-066491-1 .

Download or read book The Complexity Theory Companion written by Lane Hemaspaandra and published by Springer Science & Business Media. This book was released on 2001-12-01 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here is an accessible, algorithmically oriented guide to some of the most interesting techniques of complexity theory. The book shows that simple algorithms are at the heart of complexity theory. The book is organized by technique rather than by topic. Each chapter focuses on one technique: what it is, and what results and applications it yields.

Download or read book Randomness in Complexity Theory and Logics written by Kord Eickmeyer and published by . This book was released on 2011 with total page 97 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Kolmogorov Complexity and Algorithmic Randomness written by A. Shen and published by American Mathematical Soc.. This book was released on 2017-11-02 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: Looking at a sequence of zeros and ones, we often feel that it is not random, that is, it is not plausible as an outcome of fair coin tossing. Why? The answer is provided by algorithmic information theory: because the sequence is compressible, that is, it has small complexity or, equivalently, can be produced by a short program. This idea, going back to Solomonoff, Kolmogorov, Chaitin, Levin, and others, is now the starting point of algorithmic information theory. The first part of this book is a textbook-style exposition of the basic notions of complexity and randomness; the second part covers some recent work done by participants of the “Kolmogorov seminar” in Moscow (started by Kolmogorov himself in the 1980s) and their colleagues. This book contains numerous exercises (embedded in the text) that will help readers to grasp the material.

Download or read book Computational Complexity written by Sanjeev Arora and published by Cambridge University Press. This book was released on 2009-04-20 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.

Download or read book Computational and Statistical Group Theory written by Robert H. Gilman and published by American Mathematical Soc.. This book was released on 2002 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a nice overview of the diversity of current trends in computational and statistical group theory. It presents the latest research and a number of specific topics, such as growth, black box groups, measures on groups, product replacement algorithms, quantum automata, and more. It includes contributions by speakers at AMS Special Sessions at The University of Nevada (Las Vegas) and the Stevens Institute of Technology (Hoboken, NJ). It is suitable for graduate students and research mathematicians interested in group theory.

Download or read book A Crude Look at the Whole written by John H. Miller and published by Basic Books. This book was released on 2016-01-05 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: A top expert explains why a social and economic understanding of complex systems will help society to anticipate and confront our biggest challenges Imagine trying to understand a stained glass window by breaking it into pieces and examining it one shard at a time. While you could probably learn a lot about each piece, you would have no idea about what the entire picture looks like. This is reductionism -- the idea that to understand the world we only need to study its pieces -- and it is how most social scientists approach their work. In A Crude Look at the Whole, social scientist and economist John H. Miller shows why we need to start looking at whole pictures. For one thing, whether we are talking about stock markets, computer networks, or biological organisms, individual parts only make sense when we remember that they are part of larger wholes. And perhaps more importantly, those wholes can take on behaviors that are strikingly different from that of their pieces. Miller, a leading expert in the computational study of complex adaptive systems, reveals astounding global patterns linking the organization of otherwise radically different structures: It might seem crude, but a beehive's temperature control system can help predict market fluctuations and a mammal's heartbeat can help us understand the "heartbeat" of a city and adapt urban planning accordingly. From enduring racial segregation to sudden stock market disasters, once we start drawing links between complex systems, we can start solving what otherwise might be totally intractable problems. Thanks to this revolutionary perspective, we can finally transcend the limits of reductionism and discover crucial new ideas. Scientifically founded and beautifully written, A Crude Look at the Whole is a powerful exploration of the challenges that we face as a society. As it reveals, taking the crude look might be the only way to truly see.

Download or read book Complexity written by M. Mitchell Waldrop and published by Open Road Media. This book was released on 2019-10-01 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: “If you liked Chaos, you’ll love Complexity. Waldrop creates the most exciting intellectual adventure story of the year” (The Washington Post). In a rarified world of scientific research, a revolution has been brewing. Its activists are not anarchists, but rather Nobel Laureates in physics and economics and pony-tailed graduates, mathematicians, and computer scientists from all over the world. They have formed an iconoclastic think-tank and their radical idea is to create a new science: complexity. They want to know how a primordial soup of simple molecules managed to turn itself into the first living cell—and what the origin of life some four billion years ago can tell us about the process of technological innovation today. This book is their story—the story of how they have tried to forge what they like to call the science of the twenty-first century. “Lucidly shows physicists, biologists, computer scientists and economists swapping metaphors and reveling in the sense that epochal discoveries are just around the corner . . . [Waldrop] has a special talent for relaying the exhilaration of moments of intellectual insight.” —The New York Times Book Review “Where I enjoyed the book was when it dove into the actual question of complexity, talking about complex systems in economics, biology, genetics, computer modeling, and so on. Snippets of rare beauty here and there almost took your breath away.” —Medium “[Waldrop] provides a good grounding of what may indeed be the first flowering of a new science.” —Publishers Weekly

Download or read book Complexity and Postmodernism written by Paul Cilliers and published by Routledge. This book was released on 2002-09-11 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Complexity and Postmodernism, Paul Cilliers explores the idea of complexity in the light of contemporary perspectives from philosophy and science. Cilliers offers us a unique approach to understanding complexity and computational theory by integrating postmodern theory (like that of Derrida and Lyotard) into his discussion. Complexity and Postmodernism is an exciting and an original book that should be read by anyone interested in gaining a fresh understanding of complexity, postmodernism and connectionism.

Download or read book Mathematics and Computation written by Avi Wigderson and published by Princeton University Press. This book was released on 2019-10-29 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography

Download or read book Algorithmic Problems of Group Theory Their Complexity and Applications to Cryptography written by Delaram Kahrobaei and published by American Mathematical Soc.. This book was released on 2015-02-25 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the AMS Special Session on Algorithmic Problems of Group Theory and Their Complexity, held January 9-10, 2013 in San Diego, CA and the AMS Special Session on Algorithmic Problems of Group Theory and Applications to Information Security, held April 6-7, 2013 at Boston College, Chestnut Hill, MA. Over the past few years the field of group-based cryptography has attracted attention from both group theorists and cryptographers. The new techniques inspired by algorithmic problems in non-commutative group theory and their complexity have offered promising ideas for developing new cryptographic protocols. The papers in this volume cover algorithmic group theory and applications to cryptography.

Download or read book Geometry and Complexity Theory written by J. M. Landsberg and published by Cambridge University Press. This book was released on 2017-09-28 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two central problems in computer science are P vs NP and the complexity of matrix multiplication. The first is also a leading candidate for the greatest unsolved problem in mathematics. The second is of enormous practical and theoretical importance. Algebraic geometry and representation theory provide fertile ground for advancing work on these problems and others in complexity. This introduction to algebraic complexity theory for graduate students and researchers in computer science and mathematics features concrete examples that demonstrate the application of geometric techniques to real world problems. Written by a noted expert in the field, it offers numerous open questions to motivate future research. Complexity theory has rejuvenated classical geometric questions and brought different areas of mathematics together in new ways. This book will show the beautiful, interesting, and important questions that have arisen as a result.

Download or read book Non commutative Cryptography and Complexity of Group theoretic Problems written by Alexei G. Myasnikov and published by American Mathematical Soc.. This book was released on 2011 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Examines the relationship between three different areas of mathematics and theoretical computer science: combinatorial group theory, cryptography, and complexity theory. It explores how non-commutative (infinite) groups can be used in public key cryptography. It also shows that there is remarkable feedback from cryptography to combinatorial group theory because some of the problems motivated by cryptography appear to be new to group theory.

Download or read book Topics in Group Theory written by Geoff Smith and published by Springer Science & Business Media. This book was released on 2000-05-15 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of groups is simultaneously a branch of abstract algebra and the study of symmetry. Designed for readers approaching the subject for the first time, this book reviews all the essentials. It recaps the basic definitions and results, including Lagranges Theorem, the isomorphism theorems and group actions. Later chapters include material on chain conditions and finiteness conditions, free groups and the theory of presentations. In addition, a novel chapter of "entertainments" demonstrates an assortment of results that can be achieved with the theoretical machinery.

Download or read book Aspects of Kolmogorov Complexity the Physics of Information written by Bradley S. Tice and published by CRC Press. This book was released on 2022-09-01 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: The research presented in Aspects of Kolmogorov Complexity addresses the fundamental standard of defining randomness as measured by a Martin-Lof level of randomness as found in random sequential binary strings. A classical study of statistics that addresses both a fundamental standard of statistics as well as an applied measure for statistical communication theory. The research points to compression levels in a random state that are greater than is found in current literature. A historical overview of the field of Kolmogorov Complexity and Algorithmic Information Theory, a subfield of Information Theory, is given as well as examples using a radix 3, radix 4, and radix 5 base numbers for both random and non-random sequential strings. The text also examines monochromatic and chromatic symbols and both theoretical and applied aspects of data compression as they relate to the transmission and storage of information. The appendix contains papers on the subject given at conferences and the references are current.ContentsTechnical topics addressed in Aspects of Kolmogorov Complexity include:• Statistical Communication Theory• Algorithmic Information Theory• Kolmogorov Complexity• Martin-Lof Randomness• Compression, Transmission and Storage of Information

Download or read book Simply Complexity written by Neil Johnson and published by Simon and Schuster. This book was released on 2009-10-01 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: The new branch of science which will reveal how to avoid the rush hour, overcome cancer, and find the perfect date What do traffic jams, stock market crashes, and wars have in common? They are all explained using complexity, an unsolved puzzle that many researchers believe is the key to predicting - and ultimately solving - everything from terrorist attacks and pandemic viruses right down to rush hour traffic congestion. Complexity is considered by many to be the single most important scientific development since general relativity and promises to make sense of no less than the very heart of the Universe. Using it, scientists can find order emerging from seemingly random interactions of all kinds, from something as simple as flipping coins through to more challenging problems such as predicting shopping habits, the patterns in modern jazz, and the growth of cancer tumours.