Theory of reaction automata: a survey

Abstract

In this paper, we survey on reaction automata theory to model and analyze the biochemical behaviors of vital reactions occurring in nature. Inspired by two notions of a reaction system initiated by Ehrenfeucht and Rozenberg in 2007 and of a multiset, reaction automata (RAs) have been proposed as computing models for accepting string languages. Given an input sequence of symbols, an RA performs its computation process as follows: at every time of receiving an input symbol, it changes the current configuration (represented by a multiset) by applying reaction rules to the multiset in a prescribed manner, for which two kinds of application manners are considered: the maximally parallel manner and the (usual) sequential manner. An RA functions as an extended finite automaton in which multisets play a role of (unbounded number of) states and the state transition is performed by applying reaction rules. We show that the computational powers of RAs are Turing universal in both manners of rule applications. The relationship between the space-bounded variants of RA and the Chomsky hierarchy is also discussed. Further, we discuss the notion of chemical reaction automata, which is a simplified variant of RAs with reaction rules that are free from inhibitor functioning. We complete this survey with a variety of related models of computing together with future research topics.

Pure reaction automata

“…We also introduce a new kind of reaction automata, called pure reaction automata. They differ from those introduced by Yokomori and Okubo (2021) in how the outcome of a reaction is defined. While classical reaction automata have permanence (i.e., the entities that are not used are preserved), in pure reaction automata the entities that are not used by any reaction are lost.…”

“…The introduction of a new manner and a new model of reaction automata raises the question of its computation power compared to the already existing models. We prove that the set of languages accepted by pure reaction automata working in a maximal reactive manner contains the set of languages accepted by standard reaction automata working in the same manner as well as the set of languages accepted by reaction automata working in a maximal parallel manner (a manner already investigated by Yokomori and Okubo (2021)).…”

“…In this section, we recall the definition of reaction automata given by Yokomori and Okubo (2021) and we introduce a new policy for enabling reactions.…”

“…We denote by En X A (T) the set of reactions from ⟨A⟩ enabled in T in manner X ∈ {mp, mr}. Remark 4 The notion of mp manner given in Definition 3 is equivalent to the one given by Yokomori and Okubo (2021). Indeed, given , ∈ A # , consider the corresponding elements a, b ∈ ⟨A⟩ , identified by…”

“…A natural way to preserve the fundamentals of reaction systems while making them a universal computational model is to allow multiplicity for the entities. More than a decade ago, the first significant step in this direction was taken by Okubo et al (2012b) with the introduction of Reaction Automata and with the successive streamline of studies on the topic (see Okubo et al 2012a;Okubo 2014;Okubo andYokomori 2015, 2018;Yokomori and Okubo 2021;Okubo et al 2022). In reaction automata, a state is a multiset of entities (thus allowing an infinite set of possible states) and reactions are modified to require multisets of reactants and products.…”