Functional Equivalence and a Cover Relation for Reaction Systems

Reaction systems are a computational model originally introduced to formalize the interactions between biochemical reactions that are the basis of the functioning of the living cell. Subsets of reactions of a reaction system define result functions which leads to a concept of functional equivalence. This equivalence in turn induces a functional cover relation on the reactions of a reaction system which captures redundancies in the system. In this paper, the functional cover relation is transferred to functional equivalence classes of sets of reactions. We introduce so-called atoms as building blocks of reactions. Atoms provide a characterization of functional equivalence classes of sets of reactions and are used to prove that the functional cover relation on functional equivalence classes of sets of reactions is a lattice.