Decomposition and factorization of chemical reaction transducers

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.