Polynomial Time Coverability Analysis in Discrete State Chemical Reaction Network Subclasses

In this paper the coverability problem of discrete state Chemical Reaction Networks (d-CRNs) is considered. We study certain sub-classes of d-CRN reaction network structures and prove that the coverability relation is implied by the reachability property in another reaction network class in which the reachability problem is proven to be decidable in polynomial time. We make use of the equivalent Petri net representation of d-CRNs and the concept of dual graph to obtain networks for which the reachability relation can be decided in polynomial time. Making use of the reachability relations of the dual graph, we provide theoretical guarantee for the coverability property in the initial network. This way sufficient condition is obtained for d-CRN coverability with polynomial time complexity. The studied sub-classes of d-CRNs include subconservative network structures, in addition, complexes composed of more than one species are allowed as well. The basic concepts and the new results are illustrated on several examples.