Non-associative Kleene algebra and temporal logics
- In earlier papers we have presented algebraic semantics of CTL and CTL*. However, they were not fully satisfactory. In particular, the treatment of the iteration operators U ("Until") and W ("While") employed ad-hoc definitions with general recursion, and their interrelation in CTL* and CTL was not set up in a very algebraic way. In this paper we use a new operator with which U and W can be described by variants of the Kleene star and omega iteration. However, the operator is neither associative nor does it have a neutral element. Therefore we present a general investigation of the star and omega for such operators in what we call iteration algebras. The relation between various semantics for CTL* and CTL can then be expressed by homomorphisms between iteration algebras, which is more satisfactory than the original approach.
| Author: | Bernhard MöllerGND, Jules DesharnaisGND |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-39164 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/3916 |
| Series (Serial Number): | Reports / Technische Berichte der Fakultät für Angewandte Informatik der Universität Augsburg (2016-08) |
| Publisher: | Institut für Informatik, Universität Augsburg |
| Place of publication: | Augsburg |
| Type: | Report |
| Language: | English |
| Date of Publication (online): | 2016/12/16 |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2016/12/20 |
| Tag: | Kleene algebra; iteration algebra; semantics; temporal logics |
| 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): |  Deutsches Urheberrecht |
