A Constant Time Algorithm for DNA Add

We present a new molecular algorithm for adding two binary numbers with n bits. Without considering the generation of input, this algorithm can be performed in O(1) in a test tube using O(n) different types of DNA strands, and the output can be detected in O(n). The output strands, prior to read out operation, can serve as the input strands for another round of addition. The algorithm can be easily extended to any other logical operation, and even for adding two decimal numbers.

[1]  R J Lipton,et al.  DNA solution of hard computational problems. , 1995, Science.

[2]  A P Mills,et al.  DNA implementation of addition in which the input strands are separate from the operator strands. , 1999, Bio Systems.

[3]  Gheorghe Paun,et al.  DNA computing, sticker systems, and universality , 1998, Acta Informatica.

[4]  Ken-ichi Matsumoto,et al.  Procedures For Logic And Arithmetic Operations With Dna Molecules , 2004, Int. J. Found. Comput. Sci..

[5]  L M Adleman,et al.  Molecular computation of solutions to combinatorial problems. , 1994, Science.

[6]  Janardan Misra,et al.  Binary Arithmetic for DNA Computers , 2002, DNA.

[7]  Clifford R. Johnson,et al.  Solution of a 20-Variable 3-SAT Problem on a DNA Computer , 2002, Science.

[8]  Gang Wu,et al.  Multiplying with DNA , 2006, Natural Computing.

[9]  Karl-Heinz Zimmermann,et al.  Efficient DNA sticker algorithms for NP-complete graph problems , 2002 .

[10]  Lloyd M. Smith,et al.  DNA computing on surfaces , 2000, Nature.

[11]  Grzegorz Rozenberg,et al.  Complementarity versus universality: Keynotes of DNA computing , 1998, Complex..

[12]  F Guarnieri,et al.  Maya Blue Paint: An Ancient Nanostructured Material , 1996, Science.

[13]  M. Ganjtabesh,et al.  DNA algorithm for an unbounded fan-in Boolean circuit. , 2005, Bio Systems.

[14]  Piotr Wasiewicz,et al.  Implementation of Data Flow Logical Operation via Self-Assembly of DNA , 1999, IPPS/SPDP Workshops.

[15]  Richard J. Lipton,et al.  On the Computational Power of DNA , 1996, Discret. Appl. Math..

[16]  Donald Beaver.  Computing with DNA , 1995, J. Comput. Biol..

[17]  Gheorghe Paun,et al.  Topics in the theory of DNA computing , 2002, Theor. Comput. Sci..