Probabilistic sticker systems

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.

Probabilistic simple splicing systems

“…It has been proven that the languages generated by probabilistic splicing system have a higher computational power as compared to the languages generated by splicing systems without any restriction on the rules as stated by Turaev et al [5]. The same result is obtained when probability is used as a restriction in sticker operation by Selvarajoo et al [6]. Hence, by applying the probability concept on splicing systems and sticker systems, we can obtain new results as well as we can use them as molecular models for stochastic processes.…”

“…In probabilistic splicing systems, probabilities are associated with the axioms (not with the rules), and the probability of the generated string from two strings is calculated by multiplication of their probabilities as shown by Turaev et al and Selvarajoo et al [5,6]. In this paper, we consider a probabilistic variant of simple splicing systems.…”

Generative capacity of sticker systems with the presence of weights

“…Besides investigating the generative power of sticker systems, some other restrictions to sticker systems have been studied [17][18][19] . These papers have shown that the generative power of a sticker system increases when some algebraic structures, probabilities and some weights are incorporated into the sticker system.…”

Variants of weighted sticker systems with different weighting spaces

“…Due to the limitation of the generative power in sticker systems, several restrictions in sticker systems have been introduced 7,8 , which show that the use of some algebraic structures and probabilities can increase the generative power of sticker systems. Some new variants of sticker systems have been introduced, called the weighted sticker systems 9 .…”