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We propose an extension of the Applied Pi–calculus by introducing nondeterministic and probabilistic choice operators. The semantics of the resulting model, in which probability and nondetermin-ism are combined, is given by Segala's Probabilistic Automata driven by schedulers which resolve the nondeterministic choice among the probability distributions over(More)
We introduce a probabilistic algorithm for the simulation of chemical reactions, which can be used as an alternative to the well-established stochastic algorithm proposed by D.T. Gillespie in the '70s. We show that the probabilistic evolution of systems derived by means of our algorithm can be compared to the stochastic time evolution of chemical reactive(More)
The Calculus of Looping Sequences (CLS) is a calculus suitable to describe biological systems and their evolution. CLS terms are constructed by starting from basic constituents and composing them by means of operators of concatenation, looping, containment and parallel composition. CLS terms can be transformed by applying rewrite rules. We give a labeled(More)
The paper presents the Stochastic Calculus of Looping Sequences (SCLS) suitable to describe microbiological systems, such as cellular pathways, and their evolution. Systems are represented by terms. The terms of the calculus are constructed by basic constituent elements and operators of sequencing, looping, containment and parallel composition. The looping(More)
Bisimulations are well–established behavioural equivalences that are widely used to study properties of computer science systems. Bisimulations assume the behaviour of systems to be described as labelled transition systems, and properties of a system can be verified by assessing its bisimilarity with a system one knows to enjoy those properties. In this(More)
The Calculus of Wrapped Compartments (CWC) is a variant of the Calculus of Looping Sequences (CLS). While keeping the same expressiveness, CWC strongly simplifies the development of automatic tools for the analysis of biological systems. The main simplification consists in the removal of the sequencing operator, thus lightening the formal treatment of the(More)
We develop a model of Parametric Probabilistic Transition Systems, where probabilities associated with transitions may be parameters. We show how to find instances of the parameters that satisfy a given property and instances that either maximize or minimize the probability of reaching a certain state. As an application, we model a probabilistic(More)