Towards Quantitative Verification of Reaction Systems

Reaction systems are a formal model for computational processes inspired by the functioning of the living cell. The key feature of this model is that its behaviour is determined by the interactions of biochemical reactions of the living cell, and these interactions are based on the mechanisms of facilitation and inhibition. The formal treatment of reaction systems is qualitative as there is no direct representation of the number of molecules involved in biochemical reactions. This paper introduces reaction systems with discrete concentrations which are an extension of reaction systems allowing for quantitative modelling. We demonstrate that although reaction systems with discrete concentrations are semantically equivalent to the original qualitative reaction systems, they provide much more succinct representations in terms of the number of molecules being used. We then define the problem of reachability for reaction systems with discrete concentrations, and provide its suitable encoding in smt, together with a verification method (bounded model checking) for reachability properties. Experimental results show that verifying reaction systems with discrete concentrations instead of the corresponding reaction systems is more efficient.