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 λ-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 λ-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 linear-bounded RAs in maximally parallel
manner is incomparable to the class of languages accepted by RAs in sequential manner.