TY  - JOUR
A1  - Desharnais, Jules
A1  - Möller, Bernhard
A1  - Tchier, Fairouz
T1  - Kleene under a modal demonic star
T2  - The Journal of Logic and Algebraic Programming
N2  - In relational semantics, the input-output semantics of a program is a relation on its set of states. We generalise this in considering elements of Kleene algebras as semantical values. In a nondeterministic context, the demonic semantics is calculated by considering the worst behaviour 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 generalisation of the while statement verification rule to nondeterministic loops. The paper generalises earlier relation-algebraic work to the setting of modal Kleene algebra, an extension of Kozen's Kleene algebra with tests that allows the internalisation of weakest liberal precondition and strongest liberal postcondition operators.
Y1  - 2006
UR  - https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/53990
UR  - https://nbn-resolving.org/urn:nbn:de:bvb:384-opus4-539907
SN  - 1567-8326
VL  - 66
IS  - 2
SP  - 127
EP  - 160
PB  - Elsevier BV
ER  -