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The bounded and precise word problems for presentations of groups

ISBN: 1470441438 ;ISBN: 9781470441432 ;EISBN: 9781470458041 ;EISBN: 1470458047 ;OCLC: 1153270295 ;LCCallNum: QA174.2.I94 2020

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Title:
The bounded and precise word problems for presentations of groups
Author: Ivanov, S. V
Subjects: Computer science {For papers involving machine computations and programs in a specific mathematical area, see Section--04 in that area} -- Algorithms {For numerical algorithms, see 65-XX; for combinat ; Computer science {For papers involving machine computations and programs in a specific mathematical area, see Section--04 in that area} -- Computing methodologies and applications -- Computer graphics ; Computer science {For papers involving machine computations and programs in a specific mathematical area, see Section--04 in that area} -- Theory of computing -- Analysis of algorithms and problem com ; Convex and discrete geometry -- Polytopes and polyhedra -- Combinatorial properties (number of faces, shortest paths, etc.) [See also 05Cxx] ; Geometric group theory [See also 05C25, 20E08, 57Mxx] ; Group theory and generalizations ; Group theory and generalizations -- Special aspects of infinite or finite groups -- Cancellation theory; application of van Kampen diagrams [See also 57M05] ; Group theory and generalizations -- Special aspects of infinite or finite groups -- Generators, relations, and presentations ; Group theory and generalizations -- Special aspects of infinite or finite groups -- Geometric group theory [See also 05C25, 20E08, 57Mxx] ; Group theory and generalizations -- Special aspects of infinite or finite groups -- Word problems, other decision problems, connections with logic and automata [See also 03B25, 03D05, 03D40, 06B25, 08 ; Presentations of groups (Mathematics) ; Special aspects of infinite or finite groups ; Word problems (Mathematics)
Description: The author introduces and studies the bounded word problem and the precise word problem for groups given by means of generators and defining relations. For example, for every finitely presented group, the bounded word problem is in NP, i.e., it can be solved in nondeterministic polynomial time, and the precise word problem is in PSPACE, i.e., it can be solved in polynomial space. The main technical result of the paper states that, for certain finite presentations of groups, which include the Baumslag-Solitar one-relator groups and free products of cyclic groups, the bounded word problem and the precise word problem can be solved in polylogarithmic space. As consequences of developed techniques that can be described as calculus of brackets, the author obtains polylogarithmic space bounds for the computational complexity of the diagram problem for free groups, for the width problem for elements of free groups, and for computation of the area defined by polygonal singular closed curves in the plane. The author also obtains polynomial time bounds for these problems.
Related Titles: Memoirs of the American Mathematical Society
Publisher: Providence, RI: American Mathematical Society
Creation Date: 2020
Format: 118
Language: English
Identifier: ISBN: 1470441438
ISBN: 9781470441432
EISBN: 9781470458041
EISBN: 1470458047
OCLC: 1153270295
LCCallNum: QA174.2.I94 2020
Source: Ebook Central Academic Complete

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The bounded and precise word problems for presentations of groups

ISBN: 1470441438 ;ISBN: 9781470441432 ;EISBN: 9781470458041 ;EISBN: 1470458047 ;OCLC: 1153270295 ;LCCallNum: QA174.2.I94 2020

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