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Periodical
ISSN: 15614042 Year: 1993 Publisher: Kishinev : Academy of sciences of Moldova, Institute of mathematics,
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Computer science --- Computer science. --- Informatics --- Science --- Moldova. --- Jumhūrīyat Mūldūf --- Mo'erduowa --- Mo'erduowa Gongheguo --- Moldavia (Republic) --- Moldavian S.S.R. --- Moldavie --- Moldavii͡ --- Moldovah --- Morudoba --- Mūldūf --- Republic of Moldova --- República de Moldova --- Republica Moldova --- Republica Moldoveneasc --- République de Moldova --- Respublika Moldavii͡ --- Respublika Moldova --- RSS Moldova --- Sovetskai͡a Sot͡sialisticheskai͡a Respublika Moldova --- Sovetskaya Sotsialisticheskaya Respublika Moldova --- Soviet Socialist Republic of Moldova --- SSR Moldova --- SSRM --- Europe --- Computer. Automation --- Mathematical Sciences --- Applied Mathematics --- discrete mathematics --- software --- artificial intelligence --- theory of computing --- natural language processing --- operations research
Book
ISBN: 9781470441432 Year: 2020 Publisher: Providence, RI : American Mathematical Society,
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"We introduce and study 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, we obtain 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. We also obtain polynomial time bounds for these problems"--
Presentations of groups (Mathematics) --- Word problems (Mathematics) --- Geometric group theory --- Problèmes des mots (mathématiques) --- Groupes, Théorie géométrique des --- 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 -- Cancellation theory; application of van Kampen diagrams [See also 57M05]. --- 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 --- 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 --- 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 --- Convex and discrete geometry -- Polytopes and polyhedra -- Combinatorial properties (number of faces, shortest paths, etc.) [See also 05Cxx]. --- Group theory and generalizations -- Special aspects of infinite or finite groups -- Geometric group theory [See also 05C25, 20E08, 57Mxx]. --- 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
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