"Modelling, Simulation and Verification of Large Biological Regulatory Networks"
KeywordsQualitative models of dynamics; Model verification; Abstract interpretation; Process Hitting (Frappes de Processus); Local Causality Graphs.
- Claude Jard (President)
- François Fages (Rapporteur)
- Serge Haddad (Rapporteur)
- Jérôme Feret (Examinateur)
- Jean-Phillipe Vert (Examinateur)
- Oliver Roux (Examinateur)
- Morgan Magnin (Examinateur)
Biological Regulatory Networks (BRN) are widely used in systems biology to model, understand and control the dynamics of production of proteins within cells. While offering a very abstract representation of biological systems, the formal analysis of such models rapidly suffers from the combinatorial explosion of the generated behaviours.
This thesis addresses the modelling, the simulation and the formal checking of large-scale BRNs through the introduction of a new framework: the Process Hitting. The simplicity of this formalism notably allows the definition of efficient static analyses of complex systems in general. Firstly, this thesis focuses on refining time features within stochastic models through the introduction of a so-called stochasticity absorption factor. Such a technique brings flexibility and a compromise between time and stochastic specifications within hybrid models. A generic (non-Markovian) simulation of process calculi is then proposed and applied to the Process Hitting. In addition to the static analysis of the fixed points of Process Hitting, this thesis develops an abstract interpretation of the Process Hitting, resulting in very efficient over- and under-approximations of discrete reachability properties. This analysis also allows the highlighting of components required to satisfy such properties, thus driving a control of the system. Having a limited theoretical complexity, this approach is promising for the analysis of very large BRNs, being then a contribution opening multiple outlooks.