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Probabilistic predicates generalize standard predicates over a state space; with probabilistic predicate transformers one thus reasons about imperative programs in terms of probabilistic pre- and postconditions. Probabilistic healthiness conditions generalize the standard ones, characterizing “real” probabilistic programs, and are based on a(More)
We define the contact homology for Legendrian submanifolds in standard contact (2n + 1)-space using moduli spaces of holomorphic disks with Lagrangian boundary conditions in complex n-space. This homology provides new invariants of Legendrian iso-topy which indicate that the theory of Legendrian isotopy is very rich. Indeed, in [4] the homology is used to(More)
The two models presented in this paper provide two diierent semantics for an extension of Dijkstra's language of guarded commands. The extended language has an additional operator , namely probabilistic choice, which makes it possible to express randomised algorithms. An earlier model by Claire Jones included probabilistic choice but not non-determinism,(More)
Jones and Plotkin give a general construction for forming a proba-bilistic powerdomain over any directed-complete partial order [Jon90, JP89]. We apply their technique to the failures/divergences semantic model for Communicating Sequential Processes [Hoa85]. The resulting probabilistic model supports a new binary operator, probabilistic choice, and retains(More)
Predicate transformers facilitate reasoning about imperative programs, including those exhibiting demonic non-deterministic choice. Probabilistic predicate transformers extend that facility to programs containing probabilistic choice, so that one can in principle determine not only whether a program is guaranteed to establish a certain result, but also its(More)
Jones and Plotkin give a general construction for forming a proba-bilistic powerdomain over any directed-complete partial order Jon90, JP89]. We apply their technique to the failures/divergences semantic model for Communicating Sequential Processes Hoa85]. The resulting probabilistic model supports a new binary operator, probabilistic choice, and retains(More)
Recent work has extended Kozen's probabilistic semantics 8, 9] to include demonic nondeterminism both at the operational 5] and the logical level 12]. That makes it now possible in principle to treat probabilistic program development with the same standards of rigour that apply, when appropriate, to imperative programming 3]. In this report we treat several(More)
In 2] a space PCSP of probabilistic processes is constructed uniformly from the standard CSP failures-divergences model. Laws of CSP are shown to be valid in PCSP also, provided they have no duplication on either side of = or v separately: thus for example A u B = B u A carries over to PCSP; but A u A = A does not, because of the duplication on its(More)