TY - JOUR

T1 - Decomposition and factorization of chemical reaction transducers

AU - Okubo, Fumiya

AU - Yokomori, Takashi

N1 - Funding Information:
The authors deeply acknowledge the referees for the careful reading and valuable comments. The work of F. Okubo was in part supported by JSPS KAKENHI Grant Number JP16K16008 . The work of T. Yokomori was in part supported by JSPS KAKENHI, Grant-in-Aid for Scientific Research (C) JP17K00021 , and by Waseda University grant for Special Research Project: 2017K-121 .

PY - 2019/7/19

Y1 - 2019/7/19

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

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U2 - 10.1016/j.tcs.2019.01.032

DO - 10.1016/j.tcs.2019.01.032

M3 - Article

AN - SCOPUS:85060576435

VL - 777

SP - 431

EP - 442

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

ER -