On the properties of language classes defined by bounded reaction automata

RAIRO-Theor. Inf. Appl.

2014

Self Cite

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 [

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Reaction automata working in sequential manner

RAIRO-Theor. Inf. Appl.

2014

Self Cite

“…Introducing the model of FAMMs has been motivated by a series of our recent work on reaction automata ( [13,14,15]) that was proposed and investigated as a new computing model of automata based on biochemical reactions. A reaction automaton is a variant of a classical model in automata theory, with unbounded memory of a multiset in the general model, where reaction rules in the form of triples consisting of reactants, inhibitors, and products are applied to a current multiset (representing a configuration) to achieve one step transition.…”

Section: Related Workmentioning

confidence: 99%

“…In a series of our previous work on reaction automata (RAs) ( [13,14,15]), we have investigated the computational capability of an RA that is formulated as a string acceptor with the multiset storage. An RA employs two types of applying reaction rules: maximally parallel manner and sequential manner in the computation process, and it has been shown that RAs have the Turing computational capability in either manner of rule applications.…”

Section: Introductionmentioning

confidence: 99%

Finite Automata with Multiset Memory: A New Characterization of Chomsky Hierarchy

Fundamenta Informaticae

Yokomori

2015

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This paper concerns new characterizations of language classes in the Chomsky hierarchy in terms of a new type of computing device called FAMM (Finite Automaton with Multiset Memory) in which a multiset of symbol objects is available for the storage of working space. Unlike the stack or the tape for a storage, the multiset might seem to be less powerful in computing task, due to the lack of positional (structural) information of stored data. We introduce the class of FAMMs of degree d (for non-negative integer d) in general form, and investigate the computing powers of some subclasses of those FAMMs. We show that the classes of languages accepted by FAMMs of degree 0, by FAMMs of degree 1, by exponentially-bounded FAMMs of degree 2, and by FAMMs of degree 2 are exactly the four classes of languages REG, CF, CS and RE in the Chomsky hierarchy, respectively. Thus, this unified view from multiset-based computing provides new insight into the computational aspects of the Chomsky hierarchy.

“…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).…”

Section: Introductionmentioning

confidence: 99%

The computational capability of chemical reaction automata

Yokomori

2015

Nat Comput

Self Cite

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.