Abstract
A model for DNA computing using the recombination behaviour of DNA molecules known as a sticker system has been introduced by Adleman in 1994. A sticker model is an abstract computational model which uses the Watson-Crick complementary principle of DNA molecules. Starting from the axioms – incomplete double stranded sequences, and iteratively using sticking operations, complete double stranded sequences are obtained. It is known that sticker systems with finite sets of axioms and sticker rules generate only regular languages. Hence, different types of restrictions have been considered to increase the computational power of sticker systems. In this paper, we introduce probabilistic sticker systems in which probabilities are initially associated with the axioms, and the probability of the generated string is computed by multiplying the probabilities of all occurrences of the initial strings used in the computation of the string.
Highlights
A sticker system is a construct of 4-tuple γγ = (VV, ρρ, AA, DD), whereVV is an alphabet, ρρ ⊆ VV × VV is the symmetric relation in VV, AA is a finite subset of axioms (WWρρ (VV)), and D is a finite set of pairs BBdd, BBuu where BBdd and BBuu are finite subsets of lower and upper stickers of the forms V#V + and V#V +, respectively
A sticker language (SL) is the language generated by a sticker system which consists of all strings formed by the set of upper strands of all complete strings derived from the axioms for which an exactly matching sequence of lower stickers can be found [5, 6]
There are few types of languages generated by sticker systems which are the one-sided sticker languages, regular sticker languages, simple sticker languages, simple one-sided sticker languages and simple regular sticker languages denoted by onesided sticker language (OSSL), RSL, SSL, SOSSL and SRSL,respectively
Summary
The first formal tool for the generation of languages from DNA recombination was introduced by Head in 1987, known as splicing systems. Another language generating model which uses the sequential recombinant behaviour (“sticker operation”) of DNA molecules is a sticker system. The sticker operation is used by Adleman in his experiment of computing a Hamiltonian path in a graph by using DNA molecules [1]. The axioms and strings generated bya sticker system are considered as encoded modelsof single and double stranded DNA molecules. The initial sequences of DNA are prolonged to the left and right, producing computations of possible arbitrary length and the process stop when a complete double stranded sequence is obtained and no sticky ends exist [2]
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