A parallel algorithmic version of the local lemma

The Lovasz Local Lemma is a tool that enables one to show that certain events hold with positive, though very small probability. It often yields existence proofs of results without supplying any efficient way of solving the corresponding algorithmic problems. J. Beck recently has found a method for converting some of these existence proofs into efficient algorithmic procedures, at the cost of losing a little in the estimates. His method does not seem to be parallelizable. Here we modify his technique and achieve an algorithmic version that can be parallelized, thus obtaining deterministic NC^l algorithms for several interesting algorithmic problems.