On the Properties of Language Classes Defined by Bounded Reaction Automata

TL;DR

This paper explores the properties of language classes defined by bounded reaction automata, introducing new models and establishing their relationships with classical language hierarchies, revealing their computational power and closure properties.

Contribution

It introduces lambda-LRAs, analyzes their closure properties, and establishes the equivalence of ERA languages with context-sensitive languages, advancing the formal understanding of reaction automata.

Findings

Lambda-LRAs form an AFL with closure properties

Languages accepted by ERAs are exactly context-sensitive languages

Any recursively enumerable language is a homomorphic image of an LRA language

Abstract

Reaction automata are a formal model that has been introduced to investigate the computing powers of interactive behaviors of biochemical reactions([14]). Reaction automata are language acceptors with multiset rewriting mechanism whose basic frameworks are based on reaction systems introduced in [4]. In this paper we continue the investigation of reaction automata with a focus on the formal language theoretic properties of subclasses of reaction automata, called linearbounded reaction automata (LRAs) and exponentially-bounded reaction automata (ERAs). Besides LRAs, we newly introduce an extended model (denoted by lambda-LRAs) by allowing lambda-moves in the accepting process of reaction, and investigate the closure properties of language classes accepted by both LRAs and lambda-LRAs. Further, we establish new relationships of language classes accepted by LRAs and by ERAs with the Chomsky hierarchy. The main results include the following : (i) the class of languages accepted by lambda-LRAs forms an AFL with additional closure properties, (ii) any recursively enumerable language can be expressed as a homomorphic image of a language accepted by an LRA, (iii) the class of languages accepted by ERAs coincides with the class of context-sensitive languages.