A probabilistic powerdomain of evaluations
Proceedings of the Fourth Annual Symposium on Logic in computer science
Probabilistic non-determinism
Power domains and second-order predicates
Theoretical Computer Science - Special volume of selected papers of the Sixth Workshop on the Mathematical Foundations of Programming Semantics, Kingston, Ont., Canada, May 1990
Probabilistic predicate transformers
ACM Transactions on Programming Languages and Systems (TOPLAS)
Partial correctness for probabilistic demonic programs
Theoretical Computer Science
A Discipline of Programming
Closure Properties of a Probabilistic Domain Construction
Proceedings of the 3rd Workshop on Mathematical Foundations of Programming Language Semantics
Power Domains and Predicate Transformers: A Topological View
Proceedings of the 10th Colloquium on Automata, Languages and Programming
Dijkstras Predicate Transformers & Smyth's Power Domaine
Proceedings of the Abstract Software Specifications, 1979 Copenhagen Winter School
CAAP '94 Proceedings of the 19th International Colloquium on Trees in Algebra and Programming
Abstraction, Refinement And Proof For Probabilistic Systems (Monographs in Computer Science)
Abstraction, Refinement And Proof For Probabilistic Systems (Monographs in Computer Science)
A domain-theoretic Banach–Alaoglu theorem
Mathematical Structures in Computer Science
Semantic Domains for Combining Probability and Non-Determinism
Electronic Notes in Theoretical Computer Science (ENTCS)
De groot duality and models of choice: Angels, demons and nature†
Mathematical Structures in Computer Science
Hi-index | 0.00 |
We investigate laws for predicate transformers for the combination of non-deterministic choice and (extended) probabilistic choice, where predicates are taken to be functions to the extended non-negative reals, or to closed intervals of such reals. These predicate transformers correspond to state transformers, which are functions to conical powerdomains, which are the appropriate powerdomains for the combined forms of non-determinism. As with standard powerdomains for non-deterministic choice, these come in three flavours – lower, upper and (order-)convex – so there are also three kinds of predicate transformers. In order to make the connection, the powerdomains are first characterised in terms of relevant classes of functionals. Much of the development is carried out at an abstract level, a kind of domain-theoretic functional analysis: one considers d-cones, which are dcpos equipped with a module structure over the non-negative extended reals, in place of topological vector spaces. Such a development still needs to be carried out for probabilistic choice per se; it would presumably be necessary to work with a notion of convex space rather than a cone.