On the Power of DNA-Computing

  title={On the Power of DNA-Computing},
  author={Diana Roo{\ss} and Klaus W. Wagner},
  journal={Inf. Comput.},
Adleman used biological manipulations with DNA strings to solve some instances of the Directed Hamiltonian Path Problem. Lipton showed how to extend this idea to solve any NP problem. We prove that exactly the problems in PNP=?p2can be solved in polynomial time using Lipton's model. Various modifications of Lipton's model, based on other DNA manipulations, are investigated systematically, and it is proved that their computational power in polynomial time can be characterized by one of the… 

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  • D. Rooß
  • Physics, Computer Science
    Proceedings 1997 27th International Symposium on Multiple- Valued Logic
  • 1997
A flood of further research on computing with molecular means in theoretical computer science was introduced and examined, concerning their computational power, their efficiency and their error resistance, in this survey.

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Strategies for the development of a peptide computer

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Volume bounded molecular computation

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Complexity theory and genetics

  • P. Pudlák
  • Computer Science
    Proceedings of IEEE 9th Annual Conference on Structure in Complexity Theory
  • 1994
A population genetics model in which the operators are effectively computable-computable in polynomial time on probabilistic Turing machines is introduced, and it is shown that a population can encode easily large amount of information from environment into genetic code and process the information as a parallel computer.

Algorithms for quantum computation: discrete logarithms and factoring

  • P. Shor
  • Computer Science
    Proceedings 35th Annual Symposium on Foundations of Computer Science
  • 1994
Las Vegas algorithms for finding discrete logarithms and factoring integers on a quantum computer that take a number of steps which is polynomial in the input size, e.g., the number of digits of the integer to be factored are given.

Introduction to the theory of complexity

1. Mathematical Preliminaries, Elements of Computability Theory, and Space-Complexity Classes: Algorithms and Complexity Classes.

Quantum complexity theory

This paper gives the first formal evidence that quantum Turing machines violate the modern (complexity theoretic) formulation of the Church--Turing thesis, and proves that bits of precision suffice to support a step computation.

Speeding up computations via molecular biology

  • R. Lipton
  • Computer Science
    DNA Based Computers
  • 1995
We show how to extend the recent result of Adleman 1] to use biological experiments to directly solve any NP problem. We, then, show how to use this method to speedup a large class of important

Quantum theory, the Church–Turing principle and the universal quantum computer

  • D. Deutsch
  • Physics, Philosophy
    Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
  • 1985
It is argued that underlying the Church–Turing hypothesis there is an implicit physical assertion. Here, this assertion is presented explicitly as a physical principle: ‘every finitely realizible