A new perspective of paramodulation complexity by solving massive 8 puzzles
This work offers an incremental method for evaluating the complexity of sliding puzzles, which could be useful for researchers in automated reasoning and puzzle design.
This paper proposes a novel method to measure the complexity of sliding puzzles, specifically 8-puzzles, using paramodulation, an automated reasoning inference method. By counting the number of clauses generated through paramodulation, they successfully distinguished the complexity of 100 generated 8-puzzles, with scores ranging from 3008 for the easiest to 48653 for the most difficult.
A sliding puzzle is a combination puzzle where a player slide pieces along certain routes on a board to reach a certain end-configuration. In this paper, we propose a novel measurement of complexity of massive sliding puzzles with paramodulation which is an inference method of automated reasoning. It turned out that by counting the number of clauses yielded with paramodulation, we can evaluate the difficulty of each puzzle. In experiment, we have generated 100 * 8 puzzles which passed the solvability checking by countering inversions. By doing this, we can distinguish the complexity of 8 puzzles with the number of generated with paramodulation. For example, board [2,3,6,1,7,8,5,4, hole] is the easiest with score 3008 and board [6,5,8,7,4,3,2,1, hole] is the most difficult with score 48653. Besides, we have succeeded to obverse several layers of complexity (the number of clauses generated) in 100 puzzles. We can conclude that proposal method can provide a new perspective of paramodulation complexity concerning sliding block puzzles.