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TR03-072 | 15th September 2003 00:00

Algorithms for SAT based on search in Hamming balls


Authors: Evgeny Dantsin, Edward Hirsch, Alexander Wolpert
Publication: 8th October 2003 15:18
Downloads: 1521


We present a simple randomized algorithm for SAT and prove an upper
bound on its running time. Given a Boolean formula F in conjunctive
normal form, the algorithm finds a satisfying assignment for F
(if any) by repeating the following: Choose an assignment A at
random and search for a satisfying assignment inside a Hamming ball
around A (the radius of the ball depends on F). We show that this
algorithm solves SAT with a small probability of error in
at most 2^{n - 0.712\sqrt{n}} steps, where
n is the number of variables in F. We also derandomize this
algorithm using covering codes instead of random assignments. The
deterministic algorithm solves SAT in
at most 2^{n - 2\sqrt{n/\log_2 n}} steps.
To the best of our knowledge, this is the first non-trivial bound
for a deterministic SAT algorithm.

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