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In this paper we present an overview of the field of deterministic approximation of Markov processes, both in discrete and continuous time. We will discuss mean field approximation of discrete time Markov chains and fluid approximation of continuous time Markov chains, considering the cases in which the deterministic limit process lives in continuous time(More)
We tackle the problem of relating models of systems (mainly biological systems) based on stochastic process algebras (SPA) with models based on differential equations. We define a syntactic procedure that translates programs written in stochastic Concurrent Constraint Programming (sCCP) into a set of Ordinary Differential Equations (ODE), and also the(More)
Stochastic models such as Continuous-Time Markov Chains (CTMC) and Stochastic Hybrid Au-tomata (SHA) are powerful formalisms to model and to reason about the dynamics of biological systems, due to their ability to capture the stochasticity inherent in biological processes. A classical question in formal modelling with clear relevance to biological modelling(More)
We define a semantics for stochastic Concurrent Constraint Programming (sCCP), a stochastic process algebra, in terms of stochas-tic hybrid automata with piecewise deterministic continuous dynamics. To each program we associate a lattice of hybrid models, parameter-ized with respect to the degree of discreteness left. We study some properties of this(More)
We present a novel approach to learn the formulae characterising the emergent behaviour of a dynamical system from system observations. At a high level, the approach starts by devising a statistical dynamical model of the system which optimally fits the observations. We then propose general optimisation strategies for selecting high support formulae (under(More)
We present an application of stochastic Concurrent Constraint Programming (sCCP) for modeling biological systems. We provide a library of sCCP processes that can be used to describe straightforwardly biological networks. In the meanwhile , we show that sCCP proves to be a general and extensible framework, allowing to describe a wide class of dynamical(More)
In this paper we investigate a potential use of fluid approximation techniques in the context of stochastic model checking of CSL formulae. We focus on properties describing the behaviour of a single agent in a (large) population of agents, exploiting a limit result known also as fast simulation. In particular, we will approximate the behaviour of a single(More)
We present a stochastic version of Concurrent Constraint Programming (CCP), where we associate a rate to each basic instruction that interacts with the constraint store. We give an operational semantic that can be provided either with a discrete or a continuous model of time. The notion of observables is discussed, both for the discrete and the continuous(More)
Continuous time Markov Chains (CTMCs) are a convenient mathematical model for a broad range of natural and computer systems. As a result, they have received considerable attention in the theoretical computer science community, with many important techniques such as model checking being now mainstream. However, most methodolo-gies start with an assumption of(More)
In this paper we focus on the relation between models of biological systems consisting of ordinary differential equations (ODE) and models written in a stochastic and concurrent paradigm (sCCP stochastic Concurrent Constraint Programming). In particular, we define a method to associate a set of ODE's to an sCCP program and a method converting ODE's into(More)