On the Parallel Tower of Hanoi Puzzle: Acyclicity and a Conditional Triangle Inequality

TL;DR

This paper introduces a parallel version of the Tower of Hanoi puzzle, proves theorems on minimal moves, and presents a denoising method for optimizing configuration sequences with potential applications in hierarchical reinforcement learning.

Contribution

It provides new theoretical insights into minimal moves in a parallel Tower of Hanoi and proposes a denoising method for sequence optimization.

Findings

Theorems on minimal walks in the parallel Tower of Hanoi

A constructive proof-based denoising method

Potential application in hierarchical reinforcement learning

Abstract

A parallel variant of the Tower of Hanoi Puzzle is described herein. Within this parallel context, two theorems on minimal walks in the state space of configurations, along with their constructive proofs, are provided. These proofs are used to describe a {\sl denoising method}: a method for identifying and eliminating sub-optimal transfers within an arbitrary, valid sequence of disk configurations (as per the rules of the Puzzle). We discuss potential applications of this method to hierarchical reinforcement learning.