TY - JOUR

T1 - Doubler and linearizer

T2 - An approach toward a unified theory for molecular computing based on DNA complementarity

AU - Onodera, Kaoru

AU - Yokomori, Takashi

PY - 2008/3/1

Y1 - 2008/3/1

N2 - Two specific mappings called doubler f d and linearizer f e are introduced to bridge between two kinds of languages. Specifically, f d maps string languages into (double-stranded) molecular languages, while f e performs the opposite mapping. Using these mappings, we obtain new characterizations for the families of sticker languages and of Watson-Crick languages, which lead to not only a unified view of the two families of languages but also provide a helpful view on the computational capability of DNA complementarity. Furthermore, we introduce a special type of a projection f pr which is composed of f d and a projection in the usual sense. We show that any recursively enumerable language L can be expressed as f pr(L m) for a minimal linear language L m. This result can be strengthened to L = f p(L s), for a specific form of minimal linear language L s, which provides a simple morphic characterization for the family of recursively enumerable languages.

AB - Two specific mappings called doubler f d and linearizer f e are introduced to bridge between two kinds of languages. Specifically, f d maps string languages into (double-stranded) molecular languages, while f e performs the opposite mapping. Using these mappings, we obtain new characterizations for the families of sticker languages and of Watson-Crick languages, which lead to not only a unified view of the two families of languages but also provide a helpful view on the computational capability of DNA complementarity. Furthermore, we introduce a special type of a projection f pr which is composed of f d and a projection in the usual sense. We show that any recursively enumerable language L can be expressed as f pr(L m) for a minimal linear language L m. This result can be strengthened to L = f p(L s), for a specific form of minimal linear language L s, which provides a simple morphic characterization for the family of recursively enumerable languages.

KW - Mapping

KW - Molecular language

KW - Recursively enumerable language

KW - Sticker system

KW - Watson-Crick finite automaton

UR - http://www.scopus.com/inward/record.url?scp=39049100567&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=39049100567&partnerID=8YFLogxK

U2 - 10.1007/s11047-007-9057-5

DO - 10.1007/s11047-007-9057-5

M3 - Article

AN - SCOPUS:39049100567

VL - 7

SP - 125

EP - 143

JO - Natural Computing

JF - Natural Computing

SN - 1567-7818

IS - 1

ER -