On the properties of language classes defined by bounded reaction automata

  • Authors:

  • Fumiya Okubo;Satoshi Kobayashi;Takashi Yokomori

  • Affiliations:

  • Graduate School of Education, Waseda University, 1-6-1 Nishiwaseda, Shinjuku-ku, Tokyo 169-8050, Japan;Graduate School of Informatics and Engineering, University of Electro-Communications, 1-5-1 Chofugaoka, Chofu-shi, Tokyo 182-8585, Japan;Department of Mathematics, Faculty of Education and Integrated Arts and Sciences, Waseda University, 1-6-1 Nishiwaseda, Shinjuku-ku, Tokyo 169-8050, Japan

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2012

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Abstract

Reaction automata are a formal model that has been introduced to investigate the computing powers of interactive behaviors of biochemical reactions (Okubo et al. (2012) [19]). Reaction automata are language acceptors with multiset rewriting mechanism whose basic frameworks are based on reaction systems introduced in Ehrenfeucht and Rozenberg (2007) [8]. 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 linear-bounded reaction automata (LRAs) and exponentially-bounded reaction automata (ERAs). Besides LRAs, we newly introduce an extended model (denoted by @l-LRAs) by allowing @l-moves in the accepting process of reaction, and investigate the closure properties of language classes accepted by both LRAs and @l-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 @l-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.