A new perspective of paramodulation complexity by solving massive 8 puzzles

TL;DR

This paper introduces a novel way to measure the complexity of massive sliding puzzles using paramodulation, an automated reasoning inference method, by counting generated clauses to evaluate puzzle difficulty.

Contribution

It proposes a new complexity measurement method for sliding puzzles based on paramodulation clause counts, providing insights into puzzle difficulty levels.

Findings

Generated puzzles show a range of complexities based on clause counts.

The method distinguishes easy and difficult puzzles effectively.

Observed multiple layers of complexity in generated puzzles.

Abstract

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.