1 research outputs found
Deterministic search for CNF satisfying assignments in almost polynomial time
We consider the fundamental derandomization problem of deterministically
finding a satisfying assignment to a CNF formula that has many satisfying
assignments. We give a deterministic algorithm which, given an -variable
-clause CNF formula that has at least
satisfying assignments, runs in time for
and outputs a satisfying assignment of
. Prior to our work the fastest known algorithm for this problem was simply
to enumerate over all seeds of a pseudorandom generator for CNFs; using the
best known PRGs for CNFs [DETT10], this takes time
even for constant . Our approach is based on a new general
framework relating deterministic search and deterministic approximate counting,
which we believe may find further applications