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Stochastic Fragments: A Framework for the Exact Reduction of the Stochastic Semantics of Rule-Based Models

Jérôme Feret 1 Heinz Koeppl 2 Tatjana Petrov 2
1 ANTIQUE - Analyse Statique par Interprétation Abstraite
DI-ENS - Département d'informatique de l'École normale supérieure, Inria Paris-Rocquencourt
2 EPFL - Ecole Polytechnique Fédérale de Lausanne
Abstract : In this paper, we propose an abstract interpretation-based framework for reducing the state space of stochastic semantics for protein-protein interaction networks. Our approach consists in quotienting the state space of networks. Yet interestingly, we do not apply the widely-used strong lumpability criterion which imposes that two equivalent states behave similarly with respect to the quotient, but a weak version of it. More precisely, our framework detects and proves some invariants about the dynamics of the system: indeed the quotient of the state space is such that the probability of being in a given state knowing that this state is in a given equivalence class, is an invariant of the semantics. Then we introduce an individual-based stochastic semantics (where each agent is identified by a unique identifier) for the programs of a rule-based language (namely Kappa) and we use our abstraction framework for deriving a sound population-based semantics and a sound fragments-based semantics, which give the distribution of the traces respectively for the number of instances of molecular species and for the number of instances of partially defined molecular species. These partially defined species are chosen automatically thanks to a dependency analysis which is also described in the paper.
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https://hal.inria.fr/hal-01098561
Contributor : Jérôme Feret <>
Submitted on : Friday, December 26, 2014 - 4:20:53 PM
Last modification on : Tuesday, May 4, 2021 - 2:06:02 PM

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  • HAL Id : hal-01098561, version 1

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Jérôme Feret, Heinz Koeppl, Tatjana Petrov. Stochastic Fragments: A Framework for the Exact Reduction of the Stochastic Semantics of Rule-Based Models. International Journal of Software and Informatics (IJSI), ISCAS, 2014, Special Issue on DCM09, 7 (4), pp.527-604. ⟨hal-01098561⟩

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