Sticker systems over monoids

Molecular computing has gained many interests among researchers since Head introduced the first theoretical model for DNA based computation using the splicing operation in 1987. Another model for DNA computing was proposed by using the sticker operation which Adlemanused in his successful experiment...

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Main Authors:	Mohd Sebry, Nurul Afidah, Hamzah, Nur Zatul Akmar, Sarmin, Nor Haniza, Fong, Wan Heng, Turaev, Sherzod
Format:	Article
Language:	English
Published:	Ibnu Sina Institute for Fundamental Science Studies, Universiti Teknologi Malaysia 2012
Subjects:	QA Mathematics QA75 Electronic computers. Computer science
Online Access:	http://irep.iium.edu.my/26983/ http://irep.iium.edu.my/26983/ http://irep.iium.edu.my/26983/1/Sticker_Systems_Over_Monoids.pdf

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recordtype	eprints
spelling	iium-269832017-02-17T09:03:12Z http://irep.iium.edu.my/26983/ Sticker systems over monoids Mohd Sebry, Nurul Afidah Hamzah, Nur Zatul Akmar Sarmin, Nor Haniza Fong, Wan Heng Turaev, Sherzod QA Mathematics QA75 Electronic computers. Computer science Molecular computing has gained many interests among researchers since Head introduced the first theoretical model for DNA based computation using the splicing operation in 1987. Another model for DNA computing was proposed by using the sticker operation which Adlemanused in his successful experiment for the computation of Hamiltonian paths in a graph: a double stranded DNA sequence is composed by prolonging to the left and to the right a sequence of (single or double) symbols by using given single stranded strings or even more complex dominoes with sticky ends, gluing these ends together with the sticky ends of the current sequence according to a complementarity relation. According to this sticker operation, a language generative mechanism, called a sticker system, can be defined: a set of (incomplete) double-stranded sequences (axioms) and a set of pairs of single or double-stranded complementary sequences are given. The initial sequences are prolonged to the left and to the right by using sequences from the latter set, respectively. The iterations of these prolongations produce “computations” of possibly arbitrary length. These processes stop when a complete double stranded sequence is obtained. Sticker systems will generate only regular languages without restrictions. Additional restrictions can be imposed on the matching pairs of strands to obtain more powerful languages. Several types of sticker systems are shown to have the same power as regular grammars; one type is found to represent all linear languages whereas another one is proved to be able to represent any recursively enumerable language. The main aim of this research is to introduce and study sticker systems over monoids in which with each sticker operation, an element of a monoid is associated and a complete double stranded sequence is considered to be valid if the computation of the associated elements of the monoid produces the neutral element. Moreover, the sticker system over monoids is defined in this study. Ibnu Sina Institute for Fundamental Science Studies, Universiti Teknologi Malaysia 2012 Article PeerReviewed application/pdf en http://irep.iium.edu.my/26983/1/Sticker_Systems_Over_Monoids.pdf Mohd Sebry, Nurul Afidah and Hamzah, Nur Zatul Akmar and Sarmin, Nor Haniza and Fong, Wan Heng and Turaev, Sherzod (2012) Sticker systems over monoids. Malaysian Journal of Fundamental and Applied Sciences, 8 (3). pp. 127-132. ISSN 1823-626X http://mjfas.ibnusina.utm.my/index.php/jfs/issue/view/32/showToc
repository_type	Digital Repository
institution_category	Local University
institution	International Islamic University Malaysia
building	IIUM Repository
collection	Online Access
language	English
topic	QA Mathematics QA75 Electronic computers. Computer science
spellingShingle	QA Mathematics QA75 Electronic computers. Computer science Mohd Sebry, Nurul Afidah Hamzah, Nur Zatul Akmar Sarmin, Nor Haniza Fong, Wan Heng Turaev, Sherzod Sticker systems over monoids
description	Molecular computing has gained many interests among researchers since Head introduced the first theoretical model for DNA based computation using the splicing operation in 1987. Another model for DNA computing was proposed by using the sticker operation which Adlemanused in his successful experiment for the computation of Hamiltonian paths in a graph: a double stranded DNA sequence is composed by prolonging to the left and to the right a sequence of (single or double) symbols by using given single stranded strings or even more complex dominoes with sticky ends, gluing these ends together with the sticky ends of the current sequence according to a complementarity relation. According to this sticker operation, a language generative mechanism, called a sticker system, can be defined: a set of (incomplete) double-stranded sequences (axioms) and a set of pairs of single or double-stranded complementary sequences are given. The initial sequences are prolonged to the left and to the right by using sequences from the latter set, respectively. The iterations of these prolongations produce “computations” of possibly arbitrary length. These processes stop when a complete double stranded sequence is obtained. Sticker systems will generate only regular languages without restrictions. Additional restrictions can be imposed on the matching pairs of strands to obtain more powerful languages. Several types of sticker systems are shown to have the same power as regular grammars; one type is found to represent all linear languages whereas another one is proved to be able to represent any recursively enumerable language. The main aim of this research is to introduce and study sticker systems over monoids in which with each sticker operation, an element of a monoid is associated and a complete double stranded sequence is considered to be valid if the computation of the associated elements of the monoid produces the neutral element. Moreover, the sticker system over monoids is defined in this study.
format	Article
author	Mohd Sebry, Nurul Afidah Hamzah, Nur Zatul Akmar Sarmin, Nor Haniza Fong, Wan Heng Turaev, Sherzod
author_facet	Mohd Sebry, Nurul Afidah Hamzah, Nur Zatul Akmar Sarmin, Nor Haniza Fong, Wan Heng Turaev, Sherzod
author_sort	Mohd Sebry, Nurul Afidah
title	Sticker systems over monoids
title_short	Sticker systems over monoids
title_full	Sticker systems over monoids
title_fullStr	Sticker systems over monoids
title_full_unstemmed	Sticker systems over monoids
title_sort	sticker systems over monoids
publisher	Ibnu Sina Institute for Fundamental Science Studies, Universiti Teknologi Malaysia
publishDate	2012
url	http://irep.iium.edu.my/26983/ http://irep.iium.edu.my/26983/ http://irep.iium.edu.my/26983/1/Sticker_Systems_Over_Monoids.pdf
first_indexed	2023-09-18T20:40:07Z
last_indexed	2023-09-18T20:40:07Z
_version_	1777409308721414144

Sticker systems over monoids

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