Kleene algebra with domain

  • We propose Kleene algebra with domain (KAD), an extension of Kleene algebra with two equational axioms for a domain and a codomain operation, respectively. KAD considerably augments the expressibility of Kleene algebra, in particular for the specification and analysis of state transition systems. We develop the basic calculus, discuss some related theories and present the most important models of KAD. We demonstrate applicability by two examples: First, an algebraic reconstruction of Noethericity and well-foundedness. Second, an algebraic reconstruction of propositional Hoare logic.

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Author:Jules DesharnaisGND, Bernhard MöllerGND, Georg StruthGND
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/256
Series (Serial Number):Reports / Technische Berichte der Fakultät für Angewandte Informatik der Universität Augsburg (2003-07)
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; domain; codomain; image and preimage operation; state transition systems; program development and analysis
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