On the approximation of stochastic concurrent constraint programming by master equation.

*(English)*Zbl 1286.68344
Aldini, Alessandro (ed.) et al., Proceedings of the 6th workshop on quantitative aspects of programming languages (QAPL 2008), Budapest, Hungary, March 29–30, 2008. Amsterdam: Elsevier. Electronic Notes in Theoretical Computer Science 220, No. 3, 163-180 (2008).

Summary: We explore the relation between the stochastic semantics associated to stochastic concurrent constraint programming (sCCP) and its fluid-flow approximation. Writing the master equation for a sCCP model, we can show that the fluid flow equation is a first-order approximation of the true equation for the average. Moreover, we introduce a second-order correction and first-order equations for the variance and the covariance.

For the entire collection see [Zbl 1280.68012].

For the entire collection see [Zbl 1280.68012].

##### MSC:

68Q85 | Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.) |

34A99 | General theory for ordinary differential equations |

68Q55 | Semantics in the theory of computing |

68Q87 | Probability in computer science (algorithm analysis, random structures, phase transitions, etc.) |

92C42 | Systems biology, networks |

##### Keywords:

stochastic concurrent constraint programming; ordinary differential equations; biological systems; fluid-flow approximation##### Software:

PEPA
PDF
BibTeX
XML
Cite

\textit{L. Bortolussi}, Electron. Notes Theor. Comput. Sci. 220, No. 3, 163--180 (2008; Zbl 1286.68344)

Full Text:
DOI

##### References:

[1] | Bortolussi, L., Stochastic concurrent constraint programming, Proceedings of 4th international workshop on quantitative aspects of programming languages (QAPL’06), Entcs, 164, 65-80, (2006) |

[2] | L. Bortolussi. Constraint-based approaches to stochastic dynamics of biological systems. PhD thesis, PhD in Computer Science, University of Udine, 2007. Available at http://www.dmi.units.it/ bortolu/files/reps/Bortolussi-PhDThesis.pdf |

[3] | L. Bortolussi and A. Policriti. Dynamical systems and stochastic programming I - ordinary differential equations. Submitted to Transactions of Computational Systems Biology, 2007 · Zbl 1279.92031 |

[4] | Bortolussi, L.; Policriti, A., Stochastic concurrent constraint programming and differential equations, Proceedings of fifth workshop on quantitative aspects of programming languages, QAPL’07, Entcs, 167, (2007) · Zbl 1279.92031 |

[5] | L. Bortolussi and A. Policriti. Hybrid approximation of stochastic concurrent constraint programming. In To be presented at IFAC’08., 2008 · Zbl 1144.92001 |

[6] | Bortolussi, L.; Policriti, A., Modeling biological systems in concurrent constraint programming, Constraints, 13, 1, (2008) · Zbl 1144.92001 |

[7] | Calder, M.; Gilmore, S.; Hillston, J., Modelling the influence of RKIP on the erk signalling pathway using the stochastic process algebra PEPA, Transactions on computational systems biology, 4230, 1-23, (2006) |

[8] | L. Cardelli. From processes to ODEs by chemistry. downloadable fromhttp://lucacardelli.name/, 2006 |

[9] | L. Cardelli. A process algebra master equation. In Proceedings of QEST’07, 2007 |

[10] | Cornish-Bowden, A., Fundamentals of chemical kinetics, (2004), Portland Press |

[11] | J. Ding and J. Hillston. On odes from pepa models. In Proceedings of PASTA’07, 2007 |

[12] | N. Geisweiller, J. Hillston, and M. Stenico. Relating continuous and discrete pepa models of signalling pathways. Theoretical Computer Science, 2008. in print · Zbl 1151.68038 |

[13] | Gillespie, D.T., Exact stochastic simulation of coupled chemical reactions, J. of physical chemistry, 81, 25, (1977) |

[14] | R.A. Hayden and J.T. Bradley. Fluid-flow solutions in PEPA to the state space explosion problem. In Proceedings of PASTA’07, 2007 |

[15] | Hillston, J., A compositional approach to performance modelling, (1996), Cambridge University Press |

[16] | J. Hillston. Fluid flow approximation of PEPA models. In Proceedings of the Second International Conference on the Quantitative Evaluation of Systems (QEST’05), 2005 |

[17] | Hu, J.; Lygeros, J.; Sastry, S., Towards a theory of stochastic hybrid systems, () · Zbl 0962.93082 |

[18] | Van Kampen, N.G., Stochastic processes in physics and chemistry, (1992), Elsevier · Zbl 0511.60038 |

[19] | Norris, J.R., Markov chains, (1997), Cambridge University Press · Zbl 0873.60043 |

[20] | Regev, A.; Shapiro, E., Cellular abstractions: cells as computation, Nature, 419, (2002) |

[21] | Saraswat, V.A., Concurrent constraint programming, (1993), MIT press · Zbl 1002.68026 |

[22] | Vilar, J.M.G.; Yuan Kueh, H.; Barkai, N.; Leibler, S., Mechanisms of noise resistance in genetic oscillators, Pnas, 99, 9, 5991, (2002) |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.