Vol.:(0123456789) New Generation Computing (2022) 40:659–680 https://doi.org/10.1007/s00354-022-00160-8 123 Chemical Reaction Regular Grammars Fumiya Okubo 1  · Kaoru Fujioka 2  · Takashi Yokomori 3 Received: 26 July 2021 / Accepted: 8 February 2022 / Published online: 10 March 2022 © Ohmsha, Ltd. and Springer Japan KK, part of Springer Nature 2022 Abstract We propose a new type of computing devices based on grammatical formula- tion augmented by multiset storages, called chemical reaction regular grammars (CRRGs), and investigate some formal language theoretic characterizations of CRRGs including their generative capabilities. Shortly, a CRRG is a regular gram- mar with multisets, while its computational capability exhibits very intriguing aspects depending on the manners of rule applications. Firstly, we show that the class of languages (denoted by CRRL  ) generated by CRRGs coincides with the class of languages accepted by chemical reaction automata (Okubo and Yokomori in Nat Comput 15(2): 215–224, 2016), whose implication is that the computing power of CRRGs is also equivalent to that of several known devices introduced from dif- ferent motivations such as Petri nets (Peterson in ACM Comput Surv 9(3):223–252, 1977) and partially blind 1-way multicounter machines (Greibach in Theor Com- put Sci 7:311–324, 1979). Second, a new manner of rewriting strategy is integrated into CRRGs and we show that CRRGs working in maximal-sequential manner can generate any recursively enumerable language, which is an unexpected result with a surprise. In contrast, it is also shown that regulated controls due to regular sets and matrix constraints do not enhance the computing power of CRRGs. Third, for each k ≥ 1 a subclass of languages k-CRRL  is considered, where k is the number of diferent symbols for multisets of CRRGs. We show that the class of languages is a full principal semi-AFL, which is obtained from a characterization result that L is in k-CRRL  if L = h(g −1 (B k )∩ R) for some homomorphisms g, h, a regular set R, where B k is a paritally balanced language over k-symbol alphabet. Keywords Regular grammars · Chemical reaction automata · Multiset storages · Computational capability Mathematics Subject Classifcation 68Q42 · 68Q45 · 68Q04 * Fumiya Okubo fokubo@ait.kyushu-u.ac.jp Extended author information available on the last page of the article