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The compressed word problem for groups [electronic resource]

The compressed word problem for groups [electronic resource]

자료유형
E-Book(소장)
개인저자
Lohrey, Markus.
서명 / 저자사항
The compressed word problem for groups [electronic resource] / Markus Lohrey.
발행사항
New York, NY :   Springer New York :   Imprint: Springer,   2014.  
형태사항
1 online resource (xii, 153 p.) : ill.
총서사항
Springer briefs in mathematics,2191-8198
ISBN
9781493907489
요약
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.
일반주기
Title from e-Book title page.  
내용주기
1. Preliminaries from Theoretical Computer Science -- 2. Preliminaries from Combinatorial Group Theory -- 3. Algorithms on Compressed Words -- 4. The Compressed Word Problem -- 5. The Compressed Word Problem in Graph Products -- 6. The Compressed Word Problem in HNN-Extensions -- 7.Outlook -- References -- Index.
서지주기
Includes bibliographical references and index.
이용가능한 다른형태자료
Issued also as a book.  
일반주제명
Group theory. Word problems (Mathematics).
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020 ▼a 9781493907489
040 ▼a 211009 ▼c 211009 ▼d 211009
082 0 4 ▼a 512.2 ▼2 23
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090 ▼a 512.2
100 1 ▼a Lohrey, Markus.
245 1 4 ▼a The compressed word problem for groups ▼h [electronic resource] / ▼c Markus Lohrey.
260 ▼a New York, NY : ▼b Springer New York : ▼b Imprint: Springer, ▼c 2014.
300 ▼a 1 online resource (xii, 153 p.) : ▼b ill.
490 1 ▼a Springer briefs in mathematics, ▼x 2191-8198
500 ▼a Title from e-Book title page.
504 ▼a Includes bibliographical references and index.
505 0 ▼a 1. Preliminaries from Theoretical Computer Science -- 2. Preliminaries from Combinatorial Group Theory -- 3. Algorithms on Compressed Words -- 4. The Compressed Word Problem -- 5. The Compressed Word Problem in Graph Products -- 6. The Compressed Word Problem in HNN-Extensions -- 7.Outlook -- References -- Index.
520 ▼a 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.
530 ▼a Issued also as a book.
538 ▼a Mode of access: World Wide Web.
650 0 ▼a Group theory.
650 0 ▼a Word problems (Mathematics).
830 0 ▼a SpringerBriefs in mathematics.
856 4 0 ▼u https://oca.korea.ac.kr/link.n2s?url=http://dx.doi.org/10.1007/978-1-4939-0748-9
945 ▼a KLPA
991 ▼a E-Book(소장)

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