We develop a model of parametric probabilistic transition Systems (PPTSs), 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 non-repudiation protocol with a PPTS. The theory we develop allows us to find instances that maximize the probability that the protocol ends in a fair state (no participant has an advantage over the others).
We survey the formalism Calculus of Looping Sequences (CLS) and a number of its variants from the point of view of their use for describing biological membranes. The formalism CLS is based on term rewriting and allows describing biomolecular systems. A first variant of CLS, called Stochastic CLS, extends the formalism with stochastic time, another variant, called LCLS (CLS with links), allows describing proteins interaction at the domain level. A third variant is introduced for easier description of biological membranes. This extension can be encoded into CLS as well as other formalisms capable of membrane description such as Brane Calculi and P Systems. Such encodings allow verifying and simulating descriptions in Brane Calculi and P Systems by means of verifiers and simulators developed for CLS.
Abstract.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 nondeterminism are combined, is given by Segala's Probabilistic Automata driven by schedulers which resolve the nondeterministic choice among the probability distributions over target states. Notions of static and observational equivalence are given for the enriched calculus. In order to model the possible interaction of a process with its surrounding environment a labeled semantics is given together with a notion of weak bisimulation which is shown to coincide with the observational equivalence. Finally, we prove that results in the probabilistic framework are preserved in a purely nondeterministic setting.
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