Greedy-like algorithms in Kleene algebra

  • This paper provides an algebraic background for the formal derivation of greedy-like algorithms. Such derivations have previously been done in various frameworks including relation algebra. We propose Kleene algebra as a particularly simple alternative. Instead of converse and residuation we use modal operators that are definable in a wide class of algebras, based on domain/codomain or image/pre-image operations. By abstracting from earlier approaches we arrive at a very general theorem about the correctness of loops that covers particular forms of greedy algorithms as special cases.

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Author:Bernhard MöllerGND, Georg StruthGND
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Series (Serial Number):Reports / Technische Berichte der Fakultät für Angewandte Informatik der Universität Augsburg (2003-11)
Publisher:Institut für Informatik, Universität Augsburg
Place of publication:Augsburg
Year of first Publication:2003
Publishing Institution:Universität Augsburg
Release Date:2006/06/20
Tag:Idempotent semiring; Kleene algebra; image and preimage operation; modal operators; confluence; Geach formula; program development and analysis
GND-Keyword:Kleene-Algebra; Greedy-Algorithms
Institutes:Fakultät für Angewandte Informatik
Fakultät für Angewandte Informatik / Institut für Informatik
Fakultät für Angewandte Informatik / Institut für Informatik / Professur für Programmiermethodik und Multimediale Informationssysteme
Dewey Decimal Classification:0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 004 Datenverarbeitung; Informatik