In recent year, process algebras have been used to model biological systems. The main methods of analysis applied to these models are stochastic simulation and deterministic evaluation via ordinary differential equations, as both can be achieved without the overhead of transition system construction and the attendant state space explosion problem when considering large molecular counts. The stochastic process algebra Bio-PEPA, developed specifically for systems biology, permits concentrations to be discretised and for molecular counts to be stratified, effectively reducing the number of states and hence offering access to transition-system-based analysis techniques such as those based on continuous time Markov chains. Additionally, this allows for the definition of semantic equivalences in the process algebra tradition. In this presentation, different approaches to developing equivalences for biological modelling will be described, together with the progress that has been made in each approach. Additionally, applicability of these equivalences beyond Bio-PEPA will be discussed.
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