Robert Amador¹, Chen-Fu Chiang², and Chang-Yu Hsieh³, ^1,2State University of New York Polytechnic Institute, USA and ³Singapore-MIT Alliance for Research and Technology, USA

We designed and implemented an efficient tough random symmetric 3-SAT generator. We quantify the hardness in terms of CPU time, numbers of restarts, decisions, propagations, conflicts and conflicted literals that occur when a solver tries to solve 3-SAT instances. In this experiment, the clause variable ratio was chosen to be around the conventional critical phase transition number 4.24. The experiment shows that instances generated by our generator are significantly harder than instances generated by the Tough K-SAT generator. The difference in hardness between two SAT instance generators exponentiates as the number of Boolean variables used increases.

3-SAT, Satisfiability, Efficient Tough Random Symmetric 3-SAT Generator, Critical Phase Transition