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Entropy, search, complexity. (English) Zbl 1117.68003

Bolyai Society Mathematical Studies 16. Berlin: Springer (ISBN 978-3-540-32573-4; 978-963-9453-06-7/hbk; 978-3-540-32777-6/ebook). 264 p. (2007).
This volume presents a collection of survey papers in the field of entropy, search and complexity. Initially, the authors summarize the development in the respective fields and then present novel methodology and results. It is an innovative collection in the mentioned areas.
Publisher’s description: More than half of the papers belong to search theory, which lies on the borderline of mathematics and computer science, information theory and combinatorics, respectively. Search theory has various applications, among others in bioinformatics. Some of these papers also have links to linear statistics and communication complexity. Further works survey the fundamentals of information theory and quantum source coding. The volume is recommended to experienced researchers as well as young scientists and students both in mathematics and computer science.
Contents: Martin Aigner, “Two colors and more” (9–26); Christian Deppe, “Coding with feedback and searching with lies” (27–70); A. G. D’yachkov, A. J. Macula and P. A. Vilenkin, “Non-adaptive and trivial two-stage group testing with error-correcting \(d^e\)-disjunct inclusion matrices” (71–83); S. Ghosh, T. Shirakura and J. Srivastava, “Model identification using search linear models and search designs” (85–112); Peter Harremoës, “Information topologies with applications” (113–150); Michael Keane, “Reinforced random walk” (151–158); Dénes Petz, “Quantum source coding and data compression” (159–178); Flemming Topsøe, “Information theory at the service of science” (179–207); Paul Vitányi, “Analysis of sorting algorithms by Kolmogorov complexity” (209–232); Gábor Wiener, “Recognition problems in combinatorial search” (233–264).

MSC:

68-06 Proceedings, conferences, collections, etc. pertaining to computer science
68P10 Searching and sorting
94A17 Measures of information, entropy
60G50 Sums of independent random variables; random walks
68Q30 Algorithmic information theory (Kolmogorov complexity, etc.)
90B40 Search theory
94A15 Information theory (general)
94A29 Source coding
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