Reaction systems are a formal model that has been introduced to investigate the interactive behaviors of biochemical reactions. Based on the formal framework of reaction systems, we propose new computing models called reaction automata that feature (string) language acceptors with multiset manipulation as a computing mechanism, and show that reaction automata are computationally Turing universal. Further, some subclasses of reaction automata with space complexity are investigated and their language classes are compared to the ones in the Chomsky hierarchy. * Corresponding author level the way of emergence and evolution of biochemical functioning such as events and modules. In the same framework, they also introduced the notion of time into reaction systems and investigated notions such as reaction times, creation times of compounds and so forth. Rather recent two papers [10,11] continue the investigation of reaction systems, with the focuses on combinatorial properties of functions defined by random reaction systems and on the dependency relation between the power of defining functions and the amount of available resource.In the theory of reaction systems, a (biochemical) reaction is formulated as a triple a = (R a , I a , P a ), where R a is the set of molecules called reactants, I a is the set of molecules called inhibitors, and P a is the set of molecules called products. Let T be a set of molecules, and the result of applying a reaction a to T , denoted by res a (T ), is given by P a if a is enabled by T (i.e., if T completely includes R a and excludes I a ). Otherwise, the result is empty. Thus, res a (T ) = P a if a is enabled on T , and res a (T ) = ∅ otherwise. The result of applying a reaction a is extended to the set of reactions A, denoted by res A (T ), and an interactive process consisting of a sequence of res A (T )'s is properly introduced and investigated.In the last few decades, the notion of a multiset has frequently appeared and been investigated in many different areas such as mathematics, computer science, linguistics, and so forth. (See, e.g., [2] for the reference papers written from the viewpoint of mathematics and computer science.) The notion of a multiset has received more and more attention, particularly in the areas of biochemical computing and molecular computing (e.g., [19,23]).Motivated by these two notions of a reaction system and a multiset, in this paper we will introduce computing devices called reaction automata and show that they are computationally universal by proving that any recursively enumerable language is accepted by a reaction automaton. There are two points to be remarked: On one hand, the notion of reaction automata may be taken as a kind of an extension of reaction systems in the sense that our reaction automata deal with multisets rather than (usual) sets as reaction systems do, in the sequence of computational process. On the other hand, however, reaction automata are introduced as computing devices that accept the sets of string objects (i.e., languages over an...
