Equivalence and discretisation in Bio-PEPA

Bio-PEPA is a process algebra for modelling biological systems. An important aspect of Bio-PEPA is the ability it provides to discretise concentrations resulting in a smaller, more manageable state space. The discretisation is based on a step size which determines the size of each discrete level and also the maximum number of levels. This paper considers the relationship between two discretisations of the same Bio-PEPA model that differ only in the step size and hence the maximum number of levels, by using the idea of equivalence from concurrency and process algebra. We present a novel behavioural semantic equivalence, compression bisimulation, that equates two discretisations of the same model and we show that this equivalence is a congruence with respect to the synchronisation operator.