An experiment of the complexity of sliding block puzzles by 2D heat flow in paramodulation

TL;DR

This paper explores the complexity of sliding block puzzles using a novel 2D heat flow visualization in paramodulation, revealing patterns and groupings in puzzle difficulty through experimental analysis.

Contribution

It introduces a heat flow-based visualization method for analyzing puzzle complexity in automated reasoning with paramodulation.

Findings

Distinct heat flow patterns correlate with puzzle difficulty

Identification of puzzle groups based on heat-resisting properties

Visualization of complexity through 2D and 3D heat maps

Abstract

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.