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We provide an extension of concurrent Kleene algebras to account for probabilistic properties. The algebra yields a unified framework containing nondeterminism, concurrency and probability and is sound with respect to the set of probabilistic automata modulo probabilistic simulation. We use the resulting algebra to generalise the algebraic formulation of a… (More)

We show that a class of automata modulo simulation equivalence forms a model of probabilistic Kleene algebra. We prove completeness of this model with respect to continuous probabilistic Kleene algebras. Hence an identity is valid in continuous probabilistic Kleene algebras if and only if the associated automata are simulation equivalent.

—Hidden Markov Models, HMM's, are mathematical models of Markov processes whose state is hidden but from which information can leak via channels. They are typically represented as 3-way joint probability distributions. We use HMM's as denotations of probabilistic hidden-state sequential programs, after recasting them as " abstract " HMM's, i.e. computations… (More)

We propose a generalisation of concurrent Kleene algebra [5] that can take account of probabilistic effects in the presence of concurrency. The algebra is proved sound with respect to a model of automata modulo a variant of rooted η-simulation equivalence. Applicability is demonstrated by algebraic treatments of two examples: algebraic may testing and… (More)

We give a new true-concurrent model for probabilistic concurrent Kleene algebra. The model is based on probabilistic event structures , which combines ideas from Katoen's work on probabilistic con-currency and Varacca's probabilistic prime event structures. The event structures are compared with a true-concurrent version of Segala's prob-abilistic… (More)

In quantitative information flow we say that program Q is " at least as secure as " P just when the amount of secret information flowing from Q is never more than flows from P , with of course a suitable quantification of " flow ". This secure-refinement order is compositional just when P Q implies C(P)C(Q) for any context C, again with a suitable… (More)

Jones' rely-guarantee calculus [1] for shared variable concurrency is extended to include probabilistic behaviours. We use an algebraic approach which combines and adapts probabilistic Kleene algebras with concurrent Kleene algebra. Soundness of the algebra is shown relative to a general probabilistic event structure semantics [21]. The main contribution of… (More)

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