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This paper defines action-labelled quantitative transition systems as a general framework for combining qualitative and quantitative analysis. We define state-metrics as a natural extension of bisimulation from non-quantitative systems to quantitative ones. We then prove that any single state-metric corresponds to a bisimulation and that the greatest(More)
In 1992 Wang & Larsen extended the may- and must preorders of De Nicola and Hennessy to processes featuring probabilistic as well as nondeterministic choice. They concluded with two problems that have remained open throughout the years, namely to find complete axiomatisations and alternative characterisations for these preorders. This paper solves both(More)
Anonymity is the property of maintaining secret the identity of users performing a certain action. Anonymity protocols often use random mechanisms which can be described probabilistically. In this paper , we propose a probabilistic process calculus to describe protocols for ensuring anonymity, and we use the notion of relative entropy from information(More)
A term terminates if all its reduction sequences are of finite length. We show four type systems that ensure termination of well-typed π-calculus processes. The systems are obtained by successive refinements of the types of the simply typed π-calculus. For all (but one of) the type systems we also present upper bounds to the number of steps well-typed(More)
We develop a general testing scenario for probabilistic processes, giving rise to two theories: probabilistic may testing and probabilistic must testing. These are applied to a simple probabilistic version of the process calculus CSP. We examine the algebraic theory of probabilistic testing, and show that many of the axioms of standard testing are no longer(More)
Many behavioural equivalences or preorders for probabilistic processes involve a lifting operation that turns a relation on states into a relation on distributions of states. We show that several existing proposals for lifting relations can be reconciled to be different presentations of essentially the same lifting operation. More interestingly, this(More)
The question of equivalence has long vexed research in con-currency, leading to many different denotational-and bisimulation-based approaches; a breakthrough occurred with the insight that tests expressed within the concurrent framework itself, based on a special " success action " , yield equivalences that make only inarguable distinctions. When(More)
In this paper we propose a metric for finite processes in a probabilistic extension of CSP. The kernel of the metric corresponds to trace equivalence and most of the operators in the process algebra is shown to satisfy non-expansiveness property with respect to this metric. We also provide an algorithm to calculate the distance between two processes to a(More)
We study a process calculus which combines both nondeter-ministic and probabilistic behavior in the style of Segala and Lynch's probabilistic automata. We consider various strong and weak behavioral equivalences, and we provide complete axiomatizations for finite-state processes, restricted to guarded definitions in case of the weak equivalences. We(More)