An Experiment of the Complexity of Sliding Block Puzzles by 2d Heat Flow in Paramodulation

In this paper, we present a curious experiment with the hot list strategy in solving sliding block puzzles by paramodulation. The hot list strategy is one of the look-ahead strategies using paramodulation in automated reasoning. We define two heat flows in the reasoning process - vertical with the hot list of permutations along the Y-axis and horizontal along the X-axis. In the experiment, we have generated 500 * 8 puzzles under the test of the solvability checking by counting inversions. We have obtained curious 2D and 3D plots of the complexity by defining heat flow with hot lists. We can distinguish a few groups in 500 boards (puzzles) based on the concept of heat-resisting.