Reaction automata working in sequential manner

Abstract

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 [

The computational capability of chemical reaction automata

“…We show that CRAs in maximally parallel manner are computationally equivalent to Turing machines, while the computational power of CRAs in sequential manner coincides with that of the class of Petri nets, which is in marked contrast to the result that RAs (in both maximally parallel and sequential manners) have the computing power of Turing universality (Okubo 2014;Okubo et al 2012a). Intuitively, CRAs are defined as RAs without inhibitor functioning in each reaction, providing an offline model of computing by chemical reaction networks (CRNs).…”

“…4. Recall that the class of RAs with k-input mode in sequential manner can achieve the Turing computability [Theorem 3.1 in Okubo (2014)]. It is strongly suggested that as for the computational power, there exists a trade-off relation between the role of inhibitors in reaction rules and that of maximally parallelism in computation process of RAs.…”

“…Apart from our previous works on reaction automata (Okubo 2014;Okubo et al 2012a, b), here we refer to the following three themes of work that share subjects and issues with this paper.…”

“…CoRA; LRA; ERA mean the classes of languages accepted by RAs whose workspaces are bounded by constant, linear, exponential function, respectively. For details of the results other than Theorem 1, 2, refer to Okubo (2014), Okubo et al (2012a, b) F. Okubo, T. Yokomori either membrane structure nor a mapping component [For further reference on general subjects on multiset processing, one can find many works relevant to the current topics in Calude et al (2001)]. …”

“…In RA computation process, two manners of applying reactions are considered: maximally parallel manner and sequential manner. The investigation of RAs is continued with a focus on space bounded RAs and on sequential RAs, respectively, in Okubo et al (2012b) and Okubo (2014).…”