A compositional framework for Boolean networks

Boolean networks are a widely used qualitative approach for modelling and analysing biological systems. However, their application is restricted by the well-known state space explosion problem which means that modelling large-scale, realistic biological systems is challenging. In this paper we set out to facilitate the construction and analysis of large scale biological models by developing a formal framework for the composition of Boolean networks. The compositional approach we present is based on merging entities between Boolean networks using a binary Boolean operator and we formalise the preservation of behaviour under composition using a notion of compatibility. We investigate characterising compatibility in terms of the composed models by developing a trace alignment property. In particular, we use a formalisation of the interference that can occur in a composed model to define an extended trace alignment property that we show completely characterises compatibility.