A DNA-Based Random Walk Method for Solving k-SAT Sergio Diaz, Juan Luis Esteban and Mitsunori Ogihara

Solving k-SAT problem Using Schöning’s algorithm –Pick uniformly at random a clause that is unsatisfied currently, pick a literal from the selected clause uniformly at random, and flip the assignment to the literal to satisfy the clause

Concurrent Version of Schöning’s algorithm 1.Pick F k ( n ) random assignments as the initial search space 2.Repeat the following 2 n times 1.Test whether there is a satisfying assignment in the current pool. If so, assert that the input formula is satisfiable and halt. 2.Concurrently for each assignment a, select uniformly at random a clause C yet to be satisfied, select uniformly at random a literal y  C, and flip the bit of y in a.

Implementing Step 2 For each i, 1  i  2n, select into the test tube Q i assignments whose are to be modified to satisfy i. For each i, 1  i  2n, from each assignment in Q i create its copy with the new time stamp and with the intended modification to the assignment to i. Merge all the new assignments into one test tube. Turn that test tube into T.