### Abstract

Chemical reaction automata, computing models inspired by chemical reactions occurring in nature, have been proposed and investigated in [28]. In this paper, we introduce the notion of a chemical reaction transducer (CRT) which is defined as a chemical reaction automaton equipped with output device. We investigate the problem of decomposing CRTs into simpler component CRTs in two different forms: serial decomposition and factorization. For the serial decomposition, we give a sufficient condition for CRTs to be serially decomposable. For factorization, we show that each CRT T can be realized in the form: T(x)=g(h^{−1}(x)∩L) for some codings g,h and a chemical reaction language L, which provides a generalization of notable Nivat's Theorem for rational transducers. This result is then elaborated in a refined form. Further, some transformational characterizations of CRTs are also discussed.

Original language | English |
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Journal | Theoretical Computer Science |

DOIs | |

Publication status | Accepted/In press - 2019 Jan 1 |

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### Keywords

- Chemical reaction automata
- Chemical reaction transducers
- Decomposition theorem
- Multiset-based computing

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

**Decomposition and factorization of chemical reaction transducers.** / Okubo, Fumiya; Yokomori, Takashi.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Decomposition and factorization of chemical reaction transducers

AU - Okubo, Fumiya

AU - Yokomori, Takashi

PY - 2019/1/1

Y1 - 2019/1/1

N2 - Chemical reaction automata, computing models inspired by chemical reactions occurring in nature, have been proposed and investigated in [28]. In this paper, we introduce the notion of a chemical reaction transducer (CRT) which is defined as a chemical reaction automaton equipped with output device. We investigate the problem of decomposing CRTs into simpler component CRTs in two different forms: serial decomposition and factorization. For the serial decomposition, we give a sufficient condition for CRTs to be serially decomposable. For factorization, we show that each CRT T can be realized in the form: T(x)=g(h−1(x)∩L) for some codings g,h and a chemical reaction language L, which provides a generalization of notable Nivat's Theorem for rational transducers. This result is then elaborated in a refined form. Further, some transformational characterizations of CRTs are also discussed.

AB - Chemical reaction automata, computing models inspired by chemical reactions occurring in nature, have been proposed and investigated in [28]. In this paper, we introduce the notion of a chemical reaction transducer (CRT) which is defined as a chemical reaction automaton equipped with output device. We investigate the problem of decomposing CRTs into simpler component CRTs in two different forms: serial decomposition and factorization. For the serial decomposition, we give a sufficient condition for CRTs to be serially decomposable. For factorization, we show that each CRT T can be realized in the form: T(x)=g(h−1(x)∩L) for some codings g,h and a chemical reaction language L, which provides a generalization of notable Nivat's Theorem for rational transducers. This result is then elaborated in a refined form. Further, some transformational characterizations of CRTs are also discussed.

KW - Chemical reaction automata

KW - Chemical reaction transducers

KW - Decomposition theorem

KW - Multiset-based computing

UR - http://www.scopus.com/inward/record.url?scp=85060576435&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85060576435&partnerID=8YFLogxK

U2 - 10.1016/j.tcs.2019.01.032

DO - 10.1016/j.tcs.2019.01.032

M3 - Article

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

ER -