Roughly speaking, the Kolmogorov Complexity proof of Lovasz local lemma states that for any $k$-CNF $S$ on $n$ variables and $m$ clauses, where the dependency of every clause is bounded by $2^{k-c}$, for some constant $c$, there is a satisfying assignment which can be evaluated in polynomial time.
What is the exact (minimum) value of $c$ for which the lemma holds, and how is this derived?
Thanks in advance.