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DNA Solution of Hard Computational Problems

Learn how Adleman revolutionized problem-solving by solving the Hamiltonian path problem and introducing the concept of biocomputing using DNA molecules. Explore how NP problems can be efficiently reduced to the Hamiltonian path problem, paving the way for solving complex computational challenges faster. Discover the SAT problem and how it can be tackled using biocomputing techniques. Dive into the details of generating sequences and solving SAT problems in a step-by-step approach.

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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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