Markov chains: Computing limit existence and approximations with DNA

Cardona, Mónica; Colomer, M. Angels; Conde, Josep; Miret, Josep M.; Miró, Jesús M.; Zaragoza, Alba

doi:10.1016/j.biosystems.2005.05.003

Cited by 12 publications

(9 citation statements)

References 5 publications

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“…This P system provides the n-th power of the transition matrix associated with the Markov chain, encoding the power in the environment of a halting configuration of the system. In [1] this problem has been addressed by means of a molecular DNA based algorithms, giving an estimation of this power in polynomial time, and providing a new approach to the problem of computing the limit of a Markov chain.…”

Section: Discussionmentioning

confidence: 99%

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Handling Markov Chains with Membrane Computing

Cardona

Colomer

Pérez–Jiménez

et al. 2006

Lecture Notes in Computer Science

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Summary. In this paper we approach the problem of computing the n-th power of the transition matrix of an arbitrary Markov chain through membrane computing. The proposed solution is described in a semi-uniform way in the framework of P systems with external output. The amount of resources required in the construction is polynomial in the number of states of the Markov chain and in the power. The time of execution is linear in the power and is independent of the number of states involved in the Markov chain.

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Section: Discussionmentioning

confidence: 99%

“…This subject has been treated in [1] where two algorithms based on DNA are described that only allow us to obtain an estimation of the powers. These algorithms run in polynomial time and require a polynomial amount of resources.…”

Section: Introductionmentioning

confidence: 99%

Handling Markov Chains with Membrane Computing

Cardona

Colomer

Pérez–Jiménez

et al. 2006

Lecture Notes in Computer Science

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show abstract

“…These also allow the computation of a limit using DNA computation. The states and the transition probabilities have been encoded using strands of DNA for generating paths of the Markov chain (Cardona et al, 2005).…”

Section: Markov Chainsmentioning

confidence: 99%

DNA Computation: Applications and Perspectives

Tagore¹,

Bhattacharya²,

Islam³

et al. 2010

J Proteomics Bioinform

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The computational capability of living systems has intrigued researchers for years. Primarily, the focus has been on implementing aspects of living systems in computational devices. Computer literal peoples expand their hand to the molecular biologist and chemist to explore the potential for computation of biological molecules line Deoxyribonucleic Acid (DNA) and Ribonucleic Acid (RNA) which are information carrying molecules. In this context, DNA computation is basically a collection of specially selected DNA strands whose combinations will result in the solution to some problems. DNA computation rather DNA-based computing is at the intersection of several threads of research. Main advantages of DNA computation are miniaturization and parallelism over conventional silicon-based machines. The informationbearing capability of DNA molecules is a cornerstone of modern theories of genetics and molecular biology. In this paper we have tried to focus on some key issues regarding the used and implementation DNA-based devices in life science fi eld. We have also tried to suggest its advantage over silicon computers.

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“…In this case, it equivalence class is a singleton. So, there is no j (1 ≤ j ≤ k) such that b ij and b ji belongs to C α+2 (1). Then the rules of type (1) are not applicable for i.…”

Section: Lemmamentioning

confidence: 99%

“…The amount of resources that we use is polynomial in the number of states. This subject has been also treated in terms of DNA computing ( [1]), based on a mathematical proposition of existence rather than on the classical definition of the period of a state. This is due to the fact that DNA computing is good in detecting the existence, but it has difficulties in obtaining numerical quantifications.…”

Section: Introductionmentioning

confidence: 99%

Classifying States of a Finite Markov Chain with Membrane Computing

et al. 2006

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Abstract. In this paper we present a method to classify the states of a finite Markov chain through membrane computing. A specific P system with external output is designed for each boolean matrix associated with a finite Markov chain. The computation of the system allows us to decide the convergence of the process because it determines in the environment the classification of the states (recurrent, absorbent, and transient) as well as the periods of states. The amount of resources required in the construction is polynomial in the number of states of the Markov chain.

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Markov chains: Computing limit existence and approximations with DNA

Cited by 12 publications

References 5 publications

Handling Markov Chains with Membrane Computing

Handling Markov Chains with Membrane Computing

DNA Computation: Applications and Perspectives

Classifying States of a Finite Markov Chain with Membrane Computing

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