The Statistical Mechanics ofk
نویسنده
چکیده
The satissability of random CNF formulae with precisely k variables per clause (\k-SAT") is a popular testbed for the performance of search algorithms. Formulae have M clauses from N variables, randomly negated, keeping the ratio = M=N xed. For k = 2, this model has been proven to have a sharp threshold at = 1 between formulae which are almost aways satissable and formulae which are almost never satissable as N ! 1. Computer experiments for k = 2, 3, 4, 5 and 6, (carried out in collaboration with B. Selman of ATT Bell Labs) show similar threshold behavior for each value of k. Finite-size scaling, a theory of the critical point phenomena used in statistical physics, is shown to characterize the size dependence near the threshold. Annealed and replica-based mean eld theories give a good account of the results.
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تاریخ انتشار 1994