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100   $a20140404d2014      u|         0
101 0 $aeng
135   $aur|n|---|||||
181   $ctxt
182   $cc
183   $acr
200 14$aThe compressed word problem for groups /$fby Markus Lohrey
205   $a1st ed. 2014.
210  1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d2014.
215   $a1 online resource (161 p.)
225 1 $aSpringerBriefs in Mathematics,$x2191-8198
300   $aDescription based upon print version of record.
311   $a1-4939-0747-6 
320   $aIncludes bibliographical references and index.
327   $a1. 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.
330   $aThe Compressed Word Problem for Groups provides a detailed exposition of known results on the compressed word problem, emphasizing efficient algorithms for the compressed word problem in various groups. The author presents the necessary background along with the most recent results on the compressed word problem to create a cohesive self-contained book accessible to computer scientists as well as mathematicians. Readers will quickly reach the frontier of current research which makes the book especially appealing for students looking for a currently active research topic at the intersection of group theory and computer science. The word problem introduced in 1910 by Max Dehn is one of the most important decision problems in group theory. For many groups, highly efficient algorithms for the word problem exist. In recent years, a new technique based on data compression for providing more efficient algorithms for word problems, has been developed, by representing long words over group generators in a compressed form using a straight-line program. Algorithmic techniques used for manipulating compressed words has shown that the compressed word problem can be solved in polynomial time for a large class of groups such as free groups, graph groups and nilpotent groups. These results have important implications for algorithmic questions related to automorphism groups.
410  0$aSpringerBriefs in Mathematics,$x2191-8198
606   $aGroup theory
606   $aTopological groups
606   $aLie groups
606   $aMathematical analysis
606   $aAnalysis (Mathematics)
606   $aGroup Theory and Generalizations$3https://scigraph.springernature.com/ontologies/product-market-codes/M11078
606   $aTopological Groups, Lie Groups$3https://scigraph.springernature.com/ontologies/product-market-codes/M11132
606   $aAnalysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12007
615  0$aGroup theory.
615  0$aTopological groups.
615  0$aLie groups.
615  0$aMathematical analysis.
615  0$aAnalysis (Mathematics).
615 14$aGroup Theory and Generalizations.
615 24$aTopological Groups, Lie Groups.
615 24$aAnalysis.
676   $a512.2
700   $aLohrey$b Markus$4aut$4http://id.loc.gov/vocabulary/relators/aut$0721694
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910300154703321
996   $aCompressed word problem for groups$91410684
997   $aUNINA