Site-graph rewriting languages, such as Kappa or BNGL, offer parsimonious ways to describe highly combinatorial systems of mechanistic interactions among proteins, which may be then simulated efficiently. Modelling mechanisms involving counting (a number of phosphorylated sites for instance) require an exponential number of rules in Kappa, and may not be simulated efficiently in BNGL.

In this paper, we extend Kappa to deal both parsimoniously and efficiently with counters. We propose a single push-out semantics for Kappa with counters, we show how to compile Kappa with counters into Kappa without counters (without requiring more rules, nor damaging the performance of the simulation), and we design a static analysis, based on affine relationships, to relate the value of each counter to their meaning and bound their values.