DNA based algorithms for solving both MAX-SAT and MAX-W-SAT problems

In this paper, we propose three DNA algorithms for the weighted maximum satisfiability problem (MAX-W-SAT for short). The first one is an extension of Lipton´s algorithm for SAT. The space solution is represented by a graph and the weights are encoded in form of pieces which are appended to the double strands representing the solutions. The second algorithm proposes a different encoding of information (clauses and weights) aiming at reducing the quantity of DNA required, and the last one proposes to represent all the weights by fixed length DNA sequences and using molecular beacons to access them. The designed algorithms solve MAX-SAT problem by assuming all the clauses having the same weight.