[PDF] The Compressed Word Problem For Groups eBook

Author : Markus Lohrey
Publisher : Springer Science & Business Media
Page : 193 pages
File Size : 35,20 MB
Release : 2014-04-04
Category : Mathematics
ISBN : 1493907484

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The Compressed Word Problem for Groups provides a detailed exposition of known results on the compressed word problem, emphasizing efficient algorithms for the compressed word problem in various groups. The author presents the necessary background along with the most recent results on the compressed word problem to create a cohesive self-contained book accessible to computer scientists as well as mathematicians. Readers will quickly reach the frontier of current research which makes the book especially appealing for students looking for a currently active research topic at the intersection of group theory and computer science. The word problem introduced in 1910 by Max Dehn is one of the most important decision problems in group theory. For many groups, highly efficient algorithms for the word problem exist. In recent years, a new technique based on data compression for providing more efficient algorithms for word problems, has been developed, by representing long words over group generators in a compressed form using a straight-line program. Algorithmic techniques used for manipulating compressed words has shown that the compressed word problem can be solved in polynomial time for a large class of groups such as free groups, graph groups and nilpotent groups. These results have important implications for algorithmic questions related to automorphism groups.

Author : Frédérique Bassino
Publisher : Walter de Gruyter GmbH & Co KG
Page : 412 pages
File Size : 46,1 MB
Release : 2020-06-08
Category : Mathematics
ISBN : 3110667525

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Detailed Description

Author : Mikhail Volkov
Publisher : Springer Science & Business Media
Page : 430 pages
File Size : 41,39 MB
Release : 2007-08-15
Category : Computers
ISBN : 3540745092

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This book features the refereed proceedings of the 2nd International Symposium on Computer Science in Russia held in September 2007. The 35 papers cover theory track deals with algorithms, protocols, and data structures; complexity and cryptography; formal languages, automata and their applications to computer science; computational models and concepts; proof theory; and applications of logic to computer science. Many applications are presented.

Author : Liesbeth De Mol
Publisher : Springer Nature
Page : 506 pages
File Size : 42,54 MB
Release : 2021-07-01
Category : Computers
ISBN : 3030800490

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This book constitutes the proceedings of the 17th Conference on Computability in Europe, CiE 2021, organized by the University of Ghent in July 2021. Due to COVID-19 pandemic the conference was held virtually. The 48 full papers presented in this volume were carefully reviewed and selected from 50 submissions. CiE promotes the development of 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 2021 had as its motto Connecting with Computability, a clear acknowledgement of the connecting and interdisciplinary nature of the conference series which is all the more important in a time where people are more than ever disconnected from one another due to the COVID-19 pandemic.

Author : Alexei G. Myasnikov
Publisher : American Mathematical Soc.
Page : 402 pages
File Size : 10,70 MB
Release : 2011
Category : Computers
ISBN : 0821853600

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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.

Author : Benjamin Steinberg
Publisher : Walter de Gruyter GmbH & Co KG
Page : 589 pages
File Size : 40,13 MB
Release : 2024-10-21
Category : Mathematics
ISBN : 3110984520

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This reference discusses how automata and language theory can be used to understand solutions to solving equations in groups and word problems in groups. Examples presented include, how Fine scale complexity theory has entered group theory via these connections and how cellular automata, has been generalized into a group theoretic setting. Chapters written by experts in group theory and computer science explain these connections.

Author : Filip Murlak
Publisher : Springer
Page : 630 pages
File Size : 38,5 MB
Release : 2011-08-09
Category : Computers
ISBN : 364222993X

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This volume constitutes the refereed proceedings of the 36th International Symposium on Mathematical Foundations of Computer Science, MFCS 2011, held in Warsaw, Poland, in August 2011. The 48 revised full papers presented together with 6 invited talks were carefully reviewed and selected from 129 submissions. Topics covered include algorithmic game theory, algorithmic learning theory, algorithms and data structures, automata, grammars and formal languages, bioinformatics, complexity, computational geometry, computer-assisted reasoning, concurrency theory, cryptography and security, databases and knowledge-based systems, formal specifications and program development, foundations of computing, logic in computer science, mobile computing, models of computation, networks, parallel and distributed computing, quantum computing, semantics and verification of programs, and theoretical issues in artificial intelligence.

Author : Dachuan Xu
Publisher : Springer
Page : 778 pages
File Size : 48,43 MB
Release : 2015-06-23
Category : Computers
ISBN : 3319213989

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This book constitutes the refereed proceedings of the 21st International Conference on Computing and Combinatorics, COCOON 2015, held in Beijing, China, in August 2015. The 49 revised full papers and 11 shorter papers presented were carefully reviewed and selected from various submissions. The papers cover various topics including algorithms and data structures; algorithmic game theory; approximation algorithms and online algorithms; automata, languages, logic and computability; complexity theory; computational learning theory; cryptography, reliability and security; database theory, computational biology and bioinformatics; computational algebra, geometry, number theory, graph drawing and information visualization; graph theory, communication networks, optimization and parallel and distributed computing.

Author : Evripidis Bampis
Publisher : Springer Nature
Page : 476 pages
File Size : 42,86 MB
Release : 2021-09-11
Category : Computers
ISBN : 3030865932

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This book constitutes the proceedings of the 23rd International Symposium on Fundamentals of Computation Theory, FCT 2021, held in Athens, Greece, in September 2021. The 30 full papers included in this volume were carefully reviewed and selected from 94 submissions. In addition, the book contains 2 invited talks. The papers cover topics of all aspects of theoretical computer science, in particular algorithms, complexity, formal and logical methods.

Author : Volker Diekert
Publisher : Walter de Gruyter GmbH & Co KG
Page : 322 pages
File Size : 24,22 MB
Release : 2024-10-07
Category : Mathematics
ISBN : 3111474275

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This book contains surveys and research articles on the state-of-the-art in finitely presented groups for researchers and graduate students. Overviews of current trends in exponential groups and of the classification of finite triangle groups and finite generalized tetrahedron groups are complemented by new results on a conjecture of Rosenberger and an approximation theorem. A special emphasis is on algorithmic techniques and their complexity, both for finitely generated groups and for finite Z-algebras, including explicit computer calculations highlighting important classical methods. A further chapter surveys connections to mathematical logic, in particular to universal theories of various classes of groups, and contains new results on countable elementary free groups. Applications to cryptography include overviews of techniques based on representations of p-groups and of non-commutative group actions. Further applications of finitely generated groups to topology and artificial intelligence complete the volume. All in all, leading experts provide up-to-date overviews and current trends in combinatorial group theory and its connections to cryptography and other areas.