Normal design algebra

  • We generalise the designs of Unifying Theories of Programming (UTP) by defining them as matrices over semirings with ideals. This clarifies the algebraic structure of designs and considerably simplifies reasoning about them, e.g., forming a Kleene and omega algebra of designs. Moreover, we prove a generalised fixpoint theorem for isotone functions on designs. We apply our framework to investigate symmetric linear recursion and its relation to tail-recursion; this substantially involves Kleene and omega algebra as well as additional algebraic formulations of determinacy, invariants, domain, pre-image, convergence and noetherity. Due to the uncovered algebraic structure of UTP designs, all our general results also directly apply to UTP.

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Author:Walter Guttmann, Bernhard MöllerGND
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Series (Serial Number):Reports / Technische Berichte der Fakultät für Angewandte Informatik der Universität Augsburg (2006-28)
Publisher:Institut für Informatik, Universität Augsburg
Place of publication:Augsburg
Year of first Publication:2006
Publishing Institution:Universität Augsburg
Release Date:2006/12/14
Tag:UTP; semiring; Kleene algebra; omega algebra; fixpoint; linear recursion
GND-Keyword:Kleene-Algebra; Halbring
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