Unique k-SAT and General k-SAT

Years and Authors of Summarized Original Work

• 2011; Hertli

Problem Definition

A Boolean formula F is said to be in conjunctive normal form (CNF) if it is a conjunction of disjunction of literals. If furthermore every disjunction (called clause) is over at most k literals, F is said to be in k-CNF. k-SAT, the decision problem whether a k-CNF formula admits a satisfying assignment, is one of the most prominent NP-complete problems. A special case of k-SAT is (promise) unique k-SAT, where the k-CNF is additionally promised to have either a unique or no satisfying assignment.

Suppose F has n variables. The trivial algorithm tries all 2ⁿ satisfying assignments. For k-SAT and especially 3-SAT, there have been many successive improvements [3–9, 11]. The best of them are randomized in the sense that they always correctly report unsatisfiability but might fail to report satisfiability with probability $\frac{1} {3}$, say.

Problem 1 ( k-SAT)

Input::

A k-CNF formula F.

Output::

...