Recent experiments by Braich et al. solving the Satisfiability Problem have demonstrated that Acrydite can be used in DNA computing to implement the extraction operation.
The cavity method has played and is playing a major role in the solution of optimization problems like the K-satisfiability and the graph coloring in present days.
3-SAT is NP-complete (like any other k-SAT problem with k>2) while 2-SAT is known to have solutions in polynomial time.