TY  - RPRT
A1  - Ehm, Thorsten
A1  - Möller, Bernhard
A1  - Struth, Georg
T1  - Kleene modules
N2  - We propose axioms for Kleene modules (KM). These structures have a Kleene algebra K and a Boolean algebra B as sorts. The scalar products are mappings K x B -> B; they arise as algebraic abstractions of relational image and preimage operations. KM is the basis of algebraic variants of dynamic logics. We develop a calculus for KM and discuss its relation to Kleene algebra with domain and to dynamic and test algebras. As an example, we apply KM to the reachability analysis in directed graphs. Keywords: Idempotent semirings, Kleene algebra, propositional dynamic logic, dynamic and test algebra, image and preimage operation, state transition systems, program development and analysis, graph algorithms
T3  - Reports / Technische Berichte der Fakultät für Angewandte Informatik der Universität Augsburg - 2003-10 
KW  - Kleene-Algebra
KW  - Idempotent semirings
KW  - Kleene algebra
KW  - propositional dynamic logic
KW  - dynamic and test algebra
Y1  - 2006
UR  - https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/189
UR  - https://nbn-resolving.org/urn:nbn:de:bvb:384-opus4-1401
PB  - Institut für Informatik, Universität Augsburg
CY  - Augsburg
ER  -