Comparing reactions in reaction systems

Originally, reaction systems were introduced to describe in a formal way the interactions between biochemical reactions taking place in living cells. They are also investigated as an abstract model of interactive computation. A reaction system is determined by a finite background set of entities and a finite set of reactions. Each reaction specifies the entities that it needs to be able to occur, the entities which block its execution, and the entities that it produces if it occurs. Based on the entities available in a state of the system, all reactions of the system that are enabled take place and together produce the entities that form the next state. In this paper we compare reactions in terms of their enabledness and results. We investigate three partial orders on reactions that build on two definitions of equivalence of (sets of) reactions. It is demonstrated how each partial order defines a lattice (with greatest lower bounds and least upper bounds) for all nontrivial reactions. Together, these orders provide an insight in possible redundancies and (re)combinations of the reactions of a reaction system. (C) 2020 Elsevier B.V. All rights reserved.Algorithms and the Foundations of Software technolog