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 present a new semantics of Statecharts that excludes failures and a compositional formulation of this semantics based on Labelled Transition Systems (LTS). We consider a hierarchy of LTS equivalences and we study their congruence properties w.r. to statechart operators

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.

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Abstract. Delays in biological systems may be used to model events for which the underlying dynamics cannot be precisely observed. Mathematical modeling of biological systems with delays is usually based on Delay Differential Equations (DDEs), a kind of differential equations in which the derivative of the unknown function at a certain time is given in terms of the values of the function at previous times. In the literature, delay stochastic simulation algorithms have been proposed. These algorithms follow a "delay as duration" approach, which is not suitable for biological systems in which species involved in a delayed interaction can be involved at the same time in other interactions. We show on a DDE model of tumor growth that the delay as duration approach for stochastic simulation is not precise, and we propose a simulation algorithm based on a "purely delayed" interpretation of delays which provides better results on the considered model. Moreover, we give a formal definition of a stochastic simulation algorithm which combines both the delay as duration approach and the purely delayed approach.