TY  - RPRT
A1  - Möller, Bernhard
A1  - Desharnais, Jules
T1  - Non-associative Kleene algebra and temporal logics
N2  - 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.
T3  - Reports / Technische Berichte der Fakultät für Angewandte Informatik der Universität Augsburg - 2016-08 
KW  - temporal logics
KW  - semantics
KW  - Kleene algebra
KW  - iteration algebra
Y1  - 2016
UR  - https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/3916
UR  - https://nbn-resolving.org/urn:nbn:de:bvb:384-opus4-39164
PB  - Institut für Informatik, Universität Augsburg
CY  - Augsburg
ER  -