The computational capability of chemical reaction automata

Abstract

We propose a new computing model called chemical reaction automata (CRAs) as a simplified variant of reaction automata (RAs) studied in recent literature (Okubo in RAIRO Theor Inform Appl 48:23---38 2014; Okubo et al. in Theor Comput Sci 429:247---257 2012a, Theor Comput Sci 454:206---221 2012b). 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). Thus, the main results in this paper not only strengthen the previous result on Turing computability of RAs but also clarify the computing powers of inhibitors in RA computation.