Kleene modules

  • We propose axioms for Kleene modules (KM). These structures have a Kleene algebra K and a Boolean algebra B as sorts. The scalar products are mappings K x B -> B; they arise as algebraic abstractions of relational image and preimage operations. KM is the basis of algebraic variants of dynamic logics. We develop a calculus for KM and discuss its relation to Kleene algebra with domain and to dynamic and test algebras. As an example, we apply KM to the reachability analysis in directed graphs. Keywords: Idempotent semirings, Kleene algebra, propositional dynamic logic, dynamic and test algebra, image and preimage operation, state transition systems, program development and analysis, graph algorithms

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Author:Thorsten EhmGND, Bernhard MöllerGND, Georg StruthGND
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/189
Series (Serial Number):Reports / Technische Berichte der Fakultät für Angewandte Informatik der Universität Augsburg (2003-10)
Publisher:Institut für Informatik, Universität Augsburg
Place of publication:Augsburg
Year of first Publication:2003
Publishing Institution:Universität Augsburg
Release Date:2006/06/07
Tag:Idempotent semirings; Kleene algebra; propositional dynamic logic; dynamic and test algebra
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