TY  - RPRT
A1  - Desharnais, Jules
A1  - Möller, Bernhard
A1  - Tchier, Fairouz
T1  - Kleene under a modal demonic star
N2  - In relational semantics, the input-output semantics of a program is a relation on its set of states. We generalize this in considering elements of Kleene algebras as semantical values. In a nondeterministic context, the demonic semantics is calculated by considering the worst behavior of the program. In this paper, we concentrate on while loops. Calculating the semantics of a loop is difficult, but showing the correctness of any candidate abstraction is much easier. For deterministic programs, Mills has described a checking method known as the while statement verification rule. A corresponding programming theorem for nondeterministic iterative constructs is proposed, proved and applied to an example. This theorem can be considered as a generalization of the while statement erification rule to nondeterministic loops. The paper generalizes earlier relation-algebraic work to the setting of modal Kleene algebra, an extension of Kozen's Kleene algebra with tests that allows the internalization of weakest liberal precondition and strongest liberal postcondition operators.
T3  - Reports / Technische Berichte der Fakultät für Angewandte Informatik der Universität Augsburg - 2004-11 
KW  - Kleene-Algebra
KW  - while loop
KW  - demonic semantics
KW  - relational abstraction
KW  - verification
KW  - Kleene algebra
KW  - rule
KW  - generalization
Y1  - 2006
UR  - https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/251
UR  - https://nbn-resolving.org/urn:nbn:de:bvb:384-opus4-2024
PB  - Institut für Informatik, Universität Augsburg
CY  - Augsburg
ER  -