Forward and Backward Bisimulations for Chemical Reaction Networks

We present two quantitative behavioral equivalences over species of a chemical reaction network(CRN) with semantics based on ordinary differential equations.Forward CRN bisimulationiden-tifies a partition where each equivalence class represents the exact sum of the concentrations ofthe species belonging to that class. Backward CRN bisimulationrelates species that have theidentical solutions at all time points when starting from the same initial conditions. Both notionscan be checked using only CRN syntactical information, i.e., by inspection of the set of reactions. We provide a unified algorithm that computes the coarsest refinement up to our bisimulationsin polynomial time. Further, we give algorithms to compute quotient CRNs induced by a bisim-ulation. As an application, we find significant reductions in a number of models of biologicalprocesses from the literature. In two cases we allow the analysis of benchmark models whichwould be otherwise intractable due to their memory requirements