Under-approximation of Reachability in Multivalued Asynchronous Networks

Abstract

Accepted at CS2Bio'13. http://cs2bio13.di.unito.it/International audienceThe Process Hitting is a recently introduced framework designed for the modelling of concurrent systems. Its originality lies in a compact representation of both components of the model and its corresponding actions: each action can modify the status of a component, and is conditioned by the status of at most one other component. This allowed to define very efficient static analysis based on local causality to compute reachability properties. However, in the case of cooperations between components (for example, when two components are supposed to interact with a third one only when they are in a given configuration), the approach leads to an over-approximated interleaving between actions, because of the pure asynchronous semantics of the model. To address this issue, we propose an extended definition of the framework, including priority classes for actions. In this paper, we focus on a restriction of the Process Hitting with two classes of priorities and a specific behaviour of the components, that is sufficient to tackle the aforementioned problem of cooperations. We show that this class of Process Hitting models allows to represent any Asynchronous Discrete Networks, either Boolean or multivalued. Then we develop a new refinement for the under-approximation of the static analysis to give accurate results for this class of Process Hitting models. Our method thus allows to efficiently under-approximate reachability properties in Asynchronous Discrete Networks; it is in particular conclusive on reachability properties in a 94 components Boolean network, which is unprecedented

Identification of biological regulatory networks from Process Hitting models

“…It is also worth noticing that the use of such intermediate sorts may trigger spurious transitions due to potential incoherences between the state of the cooperative sort and the actual state of cooperating sorts. However, such phenomena can be fixed by the use of priorities between actions [18].…”

“…This framework can be seen as a special class of formalisms like Petri Nets or Communicating Finite State Machines, where the arity and the effect of synchronizations between components are restricted. Thanks to the particular structure of interactions within a PH, very efficient static analysis methods have been developed to over-and under-approximate reachability properties making tractable the formal analysis of the qualitative dynamics of BRNs with hundreds or thousands of components, which was impossible with other state-of-the-art approaches [16][17][18].…”

Analyses statiques de la dynamique des réseaux d’automates indéterministes

“…Le théorème 23 établit une condition suffisante pour qu'un état local a j soit accessible depuis n'importe quel état délimité par un contexte donné. La preuve que nous esquissons ici est détaillée dans (Folschette et al, 2013). Cette condition repose sur l'absence de cycle dans le graphe de causalité locale simultané saturé, et sur l'indépendance de l'accessibilité des états locaux de chaque pré-condition des transitions considérées.…”

“…Nous nous focalisons sur les réseaux d'automates asynchrones de type Frappes de Processus (définition 4), c.-à-d. où le cardinal des pré-conditions des transitions est au plus deux. Nous notons toutefois que tout réseau d'automates, réseau discret, ou réseau de Petri borné peut se traduire en Frappes de Processus en conservant les points fixes (Folschette et al, 2013 ;Paulevé, 2011).…”

Kinetic Theory Modeling and Efficient Numerical Simulation of Gene Regulatory Networks Based on Qualitative Descriptions

“…Although this is a very simplistic representation of the inner kinetics of a biological process, process hitting semantics allow us to easily model interactions with only partial knowledge of the logical functions encoded therein and pave the way for powerful static analysis techniques in order to study fixed points, reachability and cut sets, which determine the minimum criteria for reachability, in spite of the present combinatorial explosion [15,16]. Examples of process hitting at work can be found in Section 3, where we use static analysis to compare the fitness of the generalized dynamics model with that of the refined model.…”