Tools and techniques for multi-valued networks using rewriting logic

Abstract

Multi-valued networks (MVNs) are an important, widely used qualitative modelling technique where time and states are discrete. MVNs extend the well-known Boolean networks by providing a more powerful qualitative modelling approach for biological systems by allowing an entity’s state to be within a range of discrete set of values instead of just 0 and 1. They provide a logical framework for qualitatively modelling and analysing control systems and have been successfully applied to biological systems and circuit design. While a range of support tools for developing and analysing MVNs exist, more work is needed to develop tools to support the practical applications of those techniques. One of the frameworks that have been successfully applied to biological systems is Rewriting Logic (RL), an algebraic specification framework that is capable of modelling and analysing the behaviour of dynamic, concurrent systems. The flexibility of RL techniques such as implementation of strategies has allowed it to be successfully used to model a wide range of different formalisms and systems, such as process algebras, Petri nets, and biological systems. RL specification, programming and computation is supported by a range of powerful analysis tools which was one of the motivations for choosing to use RL. We choose Maude as a tool in our work here which is a high-performance reflective language supporting both equational and RL specification. Maude is going to be used through this thesis to model and analyse a range of MVNs using RL. In this thesis we aim to investigate the application of RL to modelling and analysing both synchronous and asynchronous MVNs, thus enabling the application of support tools available for RL. We start by constructing an RL model for MVNs using a translation approach that translates an MVNs set of equations into rewrite rules. We formally show that our translation approach is correct by proving its soundness and completeness. We illustrate the techniques and the developed RL framework for MVNs by presenting a range of case studies which provides a good illustration of the practical application of the developed RL framework. We then introduce an artificial, scalable MVN model in order to allow a range of model sizes to be considered and we investigate the performance of our RL framework. We analyse a larger regulatory network from the literature using our RL framework to give some insights into how it coped with a larger case study