Reaction Systems, Transition Systems, and Equivalences

Abstract

Reaction systems originated as a formal model for processes inspired by the functioning of the living cell. The underlying idea of this model is that the functioning of the living cell is determined by the interactions of biochemical reactions and these interactions are based on the mechanisms of facilitation and inhibition. Since their inception, reaction systems became a well-investigated novel model of computation. Following this line of research, in this paper we discuss a systematic framework for investigating a whole range of equivalence notions for reaction systems. Some of the equivalences are defined directly on reaction systems while some are defined through transition systems associated with reaction systems. In this way we establish a new bridge between reaction systems and transition systems. In order to define equivalences which capture various ways of interacting with an environment, we also introduce models of the environment which evolve in a finite-state fashion.

Reaction Systems and Enabling Equivalence

“…• A and B are process equivalent ( [16]), denoted A ∼ PROC B, if their interactive processes are the same, i.e., PROC(A) = PROC(B).…”

“…Process equivalence is rather demanding since it relates reaction systems in all possible contexts and compares states in their entirety. For this reason, [16] considered also ways in which one might relax ∼ PROC by taking into account only those interactive processes that begin in certain designated states (∅ = Z ⊆ 2 S ), and allowing only a part (Y ⊆ S) of the background set to be 'visible' to an observer:…”

“…• A and B are Y -projection equivalent w.r.t. a set of initial states Z ( [16]), denoted A ∼ Y :Z PROC B, if we have proj Y (STS(PROC X (A))) = proj Y (STS(PROC X (B))), for every X ∈ Z.…”

“…The dynamics of reaction systems defines interactive computations (processes) that transit from state to state. In [16], we have considered various notions of equivalence for reaction systems based directly on the reaction systems as well as on the transition systems that can be associated with their computations. In this paper, we follow up on a suggestion from [16].…”

“…In [16], we have considered various notions of equivalence for reaction systems based directly on the reaction systems as well as on the transition systems that can be associated with their computations. In this paper, we follow up on a suggestion from [16]. There the (direct) equivalences were based on so-called functional equivalence.…”