Normal design algebra
- We generalise the designs of the 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, for example, since they form a Kleene and omega algebra and a test semiring. 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 |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-389793 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/38979 |
| Parent Title (English): | The Journal of Logic and Algebraic Programming |
| Publisher: | Elsevier |
| Type: | Article |
| Language: | English |
| Year of first Publication: | 2010 |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2018/07/25 |
| Volume: | 79 |
| Issue: | 2 |
| First Page: | 144 |
| Last Page: | 173 |
| DOI: | https://doi.org/10.1016/j.jlap.2009.07.002 |
| 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 |
| Licence (German): |  CC-BY-NC-ND 4.0: Creative Commons: Namensnennung - Nicht kommerziell - Keine Bearbeitung (mit Print on Demand) |
