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Groups Complexity Cryptology

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Algorithmics on SLP-compressed strings: A survey

Markus Lohrey
  • Institut für Informatik, Universität Leipzig, Augustusplatz 10–11, 04109 Leipzig, Germany
  • :
Published Online: 2012-11-27 | DOI: https://doi.org/10.1515/gcc-2012-0016

Abstract.

Results on algorithmic problems on strings that are given in a compressed form via straight-line programs are surveyed. A straight-line program is a context-free grammar that generates exactly one string. In this way, exponential compression rates can be achieved. Among others, we study pattern matching for compressed strings, membership problems for compressed strings in various kinds of formal languages, and the problem of querying compressed strings. Applications in combinatorial group theory and computational topology and to the solution of word equations are discussed as well. Finally, extensions to compressed trees and pictures are considered.

Keywords: Algorithms for compressed strings; compressed word problems; computational complexity


Received: 2012-06-06

Published Online: 2012-11-27

Published in Print: 2012-12-01


Citation Information: . Volume 4, Issue 2, Pages 241–299, ISSN (Online) 1869-6104, ISSN (Print) 1867-1144, DOI: https://doi.org/10.1515/gcc-2012-0016, November 2012

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