Abstracting Asynchronous Multi-Valued Networks

Multi-valued networks (MVNs) provide a simple yet expressive qualitative state based modelling approach for biological systems. In this paper we develop an abstraction theory for asynchronous MVNs that allows the state space of a model to be reduced while preserving key properties. The abstraction theory therefore provides a mechanism for coping with the state space explosion problem and supports the analysis and comparison of MVNs. We take as our starting point the abstraction theory for synchronous MVNs which uses the under- approximation approach of trace set inclusion. We show this definition of asynchronous abstraction allows the sound inference of analysis properties and preserves other interesting model properties. One problem that arises in the asynchronous case is that the trace set of an MVN can be infinite making a simple trace set inclusion check infeasible. To address this we develop a decision procedure for checking asynchronous abstractions based on using the finite state graph of an asynchronous MVN to reason about its trace semantics and formally show that this decision procedure is correct. We illustrate the abstraction techniques developed by considering two detailed case studies in which asynchronous abstractions are identified and validated for existing asynchronous MVN models taken from the literature.