REACTION AUTOMATA WORKING IN SEQUENTIAL MANNER

Based on the formal framework of reaction systems by Ehrenfeucht and Rozenberg [Fund. Inform. 75 (2007) 263-280], reaction automata (RAs) have been introduced by Okubo et al. [Theoret. Comput. Sci. 429 (2012) 247-257], as language acceptors with multiset rewriting mechanism. In this paper, we continue the investigation of RAs with a focus on the two manners of rule application: maximally parallel and sequential. Considering restrictions on the workspace and the lambda-input mode, we introduce the corresponding variants of RAs and investigate their computation powers. In order to explore Turing machines (TMs) that correspond to RAs, we also introduce a new variant of TMs with restricted workspace, called s(n)-restricted TMs. The main results include the following: (i) for a language L and a function s(n), L is accepted by an s(n)-bounded RA with lambda-input mode in sequential manner if and only if L is accepted by a log s(n)-bounded one-way TM; (ii) if a language L is accepted by a linear-bounded RA in sequential manner, then L is also accepted by a P automaton [Csuhaj-Varju and Vaszil, vol. 2597 of Lect. Notes Comput. Sci. Springer (2003) 219-233.] in sequential manner; (iii) the class of languages accepted by linearbounded RAs in maximally parallel manner is incomparable to the class of languages accepted by RAs in sequential manner.