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DNA Solution of Hard Computational Problems

DNA Solution of Hard Computational Problems. Richard J. Lipton Science, Vol.268, pp.542-545, April 1995. NP problems. Adleman solved Hamiltonian path problem. All NP problems can be efficiently reduced to HPP.  We can solve all NP problems

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DNA Solution of Hard Computational Problems

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  1. DNA Solution of Hard Computational Problems Richard J. Lipton Science, Vol.268, pp.542-545, April 1995.

  2. NP problems • Adleman solved Hamiltonian path problem. • All NP problems can be efficiently reduced to HPP.  We can solve all NP problems  But, we need more efficient way, not brute-force method. (Only can solve 70 or less node HPP.)

  3. The criterion of computing speed • How many parallel processes • Biocomputer: 3g of water  1022 molecules • How many steps each can perform per unit time • Supercomputer: 100 million op/sec • Biocomputer: limited to lab experiments.

  4. Satisfaction problem (SAT) • The SAT problem is to find Boolean values for x and y that make the formula F true.

  5. Solving SAT y x 1 1 a3 a2 a1 0 0 X’ Y’ Generating sequences similar with Adlman’s approach Sequence length = 20bp

  6. Solving SAT • Generate sequence. • t1 = E(t0, 1, 1), t1’ = E(t0, 1, 0). Pour t1 and t2 to t3. • t4 = E(t3, 1, 0), t4’ = E(t3, 1, 1). t5 = E(t4’, 2, 0). Pour t4 and t5 to t6. • Check sequence in t6

  7. Example

  8. General case • Any SAT problem on n variables and m clauses can be solved with at most order m extract steps and one detect step.

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