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53
Stochastic concurrent constraint programming
 In Proceedings of 4th International Workshop on Quantitative Aspects of Programming Languages, QAPL 2006, ENTCS
, 2006
"... 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 o ..."
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Cited by 44 (14 self)
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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 inverse procedure translating ODE’s into sCCP programs. For the class of biochemical reactions, we show that the translation is correct w.r.t. the intended rate semantics of the models. Finally, we show that the translation does not generally preserve the dynamical behavior, giving a list of open research problems in this direction.
A fluid analysis framework for a Markovian process algebra
, 2010
"... Markovian process algebras, such as PEPA and stochastic πcalculus, bring a powerful compositional approach to the performance modelling of complex systems. However, the models generated by process algebras, as with other interleaving formalisms, are susceptible to the state space explosion problem. ..."
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Cited by 41 (27 self)
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Markovian process algebras, such as PEPA and stochastic πcalculus, bring a powerful compositional approach to the performance modelling of complex systems. However, the models generated by process algebras, as with other interleaving formalisms, are susceptible to the state space explosion problem. Models with only a modest number of process algebra terms can easily generate so many states that they are all but intractable to traditional solution techniques. Previous work aimed at addressing this problem has presented a fluidflow approximation allowing the analysis of systems which would otherwise be inaccessible. To achieve this, systems of ordinary differential equations describing the fluid flow of the stochastic process algebra model are generated informally. In this paper, we show formally that for a large class of models, this fluidflow analysis can be directly derived from the stochastic process algebra model as an approximation to the mean number of component types within the model. The nature of the fluid approximation is derived and characterised by direct comparison with the Chapman–Kolmogorov equations underlying the Markov model. Furthermore, we compare the fluid approximation with the exact solution using stochastic simulation and we are able to demonstrate that it is a very accurate approximation in many cases. For the first time, we also show how to extend these techniques naturally to generate systems of differential equations approximating higher order moments of model component counts. These are important performance characteristics for estimating, for instance, the variance of the component counts. This is very necessary if we are to understand how precise the fluidflow calculation is, in a given modelling situation.
On the computational power of biochemistry
 In AB’08, volume 5147 of LNCS
, 2008
"... Abstract. We explore the computational power of biochemistry with respect to basic chemistry, identifying complexation as the basic mechanism that distinguishes the former from the latter. We use two process algebras, the Chemical Ground Form (CGF) which is equivalent to basic chemistry, and the Bio ..."
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Cited by 26 (8 self)
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Abstract. We explore the computational power of biochemistry with respect to basic chemistry, identifying complexation as the basic mechanism that distinguishes the former from the latter. We use two process algebras, the Chemical Ground Form (CGF) which is equivalent to basic chemistry, and the Biochemical Ground Form (BGF) which is a minimalistic extension of CGF with primitives for complexation. We characterize an expressiveness gap: CGF is not Turing complete while BGF supports a finite precise encoding of Random Access Machines, a wellknown Turing powerful formalism. 1
Scalable Differential Analysis of Process Algebra Models
"... The exact performance analysis of largescale software systems with discretestate approaches is difficult because of the wellknown problem of statespace explosion. This paper considers this problem with regard to the stochastic process algebra PEPA, presenting a deterministic approximation to the ..."
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Cited by 24 (8 self)
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The exact performance analysis of largescale software systems with discretestate approaches is difficult because of the wellknown problem of statespace explosion. This paper considers this problem with regard to the stochastic process algebra PEPA, presenting a deterministic approximation to the underlying Markov chain model based on ordinary differential equations. The accuracy of the approximation is assessed by means of a substantial case study of a distributed multithreaded application.
Spatial Coordination of Pervasive Services through Chemicalinspired Tuple Spaces
"... To support and engineer the spatial coordination of distributed pervasive services, we propose a chemicalinspired model, which extends tuple spaces with the ability of evolving tuples mimicking chemical systems, i.e. in terms of reaction and diffusion rules that apply to tuples modulo semantic matc ..."
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Cited by 22 (12 self)
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To support and engineer the spatial coordination of distributed pervasive services, we propose a chemicalinspired model, which extends tuple spaces with the ability of evolving tuples mimicking chemical systems, i.e. in terms of reaction and diffusion rules that apply to tuples modulo semantic match. The suitability of this model is studied considering a selfadaptive display infrastructure providing nearby people with several visualisation services (advertisements, news, personal and social content). The key result of this paper is that generalpurpose chemical reactions inspired by population dynamics can be used in pervasive applications to enact spatial computing patterns of competition and gradientbased interaction.
From processes to ODEs by Chemistry
 in TCS 2008, Fifth IFIP International Conference on Theoretical Computer Science
, 2004
"... We investigate the collective behavior of processes in terms of differential equations, using chemistry as a stepping stone. Chemical reactions can be converted to ordinary differential equations, and also to processes in a stochastic process algebra. Conversely, certain stochastic processes (in Che ..."
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Cited by 21 (0 self)
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We investigate the collective behavior of processes in terms of differential equations, using chemistry as a stepping stone. Chemical reactions can be converted to ordinary differential equations, and also to processes in a stochastic process algebra. Conversely, certain stochastic processes (in Chemical Parametric Form, or CPF) can be converted to chemical reactions. CPF is a subset of πcalculus, but is already more powerful that what is strictly needed to represent chemistry: it supports also parameterization and compositional reuse of models. The mapping of CPF to chemistry thus induces a parametric and compositional mapping of CPF to differential equations; the indirect mapping through chemistry is easier to define and understand than a direct mapping. As an example, we derive a quantitative interleaving law from the differential equations. 1
Strand Algebras for DNA Computing
, 2009
"... We present a process algebra for DNA computing, discussing compilation of other formal systems into the algebra, and compilation of the algebra into DNA structures. ..."
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Cited by 12 (1 self)
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We present a process algebra for DNA computing, discussing compilation of other formal systems into the algebra, and compilation of the algebra into DNA structures.
Termination problems in chemical kinetics
 of Lecture Notes in Computer Science
, 2008
"... Abstract. We consider nondeterministic and probabilistic termination problems in a process algebra that is equivalent to basic chemistry. We show that the existence of a terminating computation is decidable, but that termination with any probability strictly greater than zero is undecidable. Moreove ..."
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Cited by 10 (1 self)
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Abstract. We consider nondeterministic and probabilistic termination problems in a process algebra that is equivalent to basic chemistry. We show that the existence of a terminating computation is decidable, but that termination with any probability strictly greater than zero is undecidable. Moreover, we show that the fairness intrinsic in stochastic computations implies that termination of all computation paths is undecidable, while it is decidable in a nondeterministic framework. 1
Artificial biochemistry
 In Algorithmic Bioproceses, LNCS
, 2008
"... Chemical and biochemical systems are presented as collectives of interacting stochastic automata: each automaton represents a molecule that undergoes state transitions. This framework constitutes an artificial biochemistry, where automata interact by the equivalent of the law of mass action. We anal ..."
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Cited by 10 (2 self)
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Chemical and biochemical systems are presented as collectives of interacting stochastic automata: each automaton represents a molecule that undergoes state transitions. This framework constitutes an artificial biochemistry, where automata interact by the equivalent of the law of mass action. We analyze several example systems and networks, both by stochastic simulation and by ordinary dif‐ ferential equations. 1 Stochastic Automata Collectives This paper is an empirical investigation of an artifi‐ cial biochemistry obtained by the interactions of sto‐ chastic automata. The study of such artificial frame‐ works has been advocated before [2]; we explore a modern version based on a theory of concurrent processes that obeys the equivalent of the law of mass action. Foundations for this work have been investigated elsewhere [1]; here we aim to give a self‐contained and accessible presentation of the framework, and to explore by means of examples the richness of “emergent ” and unexpected behavior that can be represented by combinations of simple building blocks. By a collective we mean a large set of interacting, finite state automata. This is not quite the situation we have in classical automata theory, because we are interested in the behavior of a large set of auto‐ mata acting together. It is also not quite the situation with cellular automata, because our automata are interacting, but not necessarily on a regular grid. It is also not quite the situation in process algebra, be‐ cause again we are interested in the behavior of col‐ lectives, not of individuals. Similar frameworks have been investigated under the headings of collectives [12], sometimes including stochasticity [6]. By stochastic we mean that automata interactions have rates. Stochastic rates induce a quantitative semantics for the behavior of collectives. Collective behavior cannot be considered quite discrete, be‐ cause it can be the result of hundreds or thousands individual contributions. But it is not quite continu‐ ous either, because of the possibility of non‐trivial stochastic effects. And it is also not hybrid: there is no switching between discrete and continuous re‐ gimes.