TY  - JOUR
A1  - Höfner, Peter
A1  - Möller, Bernhard
A1  - Solin, Kim
T1  - Omega algebra, demonic refinement algebra and commands
T2  - Lecture Notes in Computer Science
N2  - Weak omega algebra and demonic refinement algebra are two ways of describing systems with finite and infinite iteration. We show that these independently introduced kinds of algebras can actually be defined in terms of each other. By defining modal operators on the underlying weak semiring, that result directly gives a demonic refinement algebra of commands. This yields models in which extensionality does not hold. Since in predicate-transformer models extensionality always holds, this means that the axioms of demonic refinement algebra do not characterise predicate-transformer models uniquely. The omega and the demonic refinement algebra of commands both utilise the convergence operator that is analogous to the halting predicate of modal μ-calculus. We show that the convergence operator can be defined explicitly in terms of infinite iteration and domain if and only if domain coinduction for infinite iteration holds.
Y1  - 2006
UR  - https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/35929
UR  - https://nbn-resolving.org/urn:nbn:de:bvb:384-opus4-359294
SN  - 0302-9743
N1  - Relations and Kleene algebra in computer science: 9th International Conference on Relational Methods in Computer Science and 4th International Workshop on Applications of Kleene Algebra, RelMiCS/AKA 2006, Manchester, UK, August/September, 2006; proceedings
VL  - 4136
SP  - 222
EP  - 234
PB  - Springer
ER  -