English

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

Combinatorics 2022-06-13 v3 Discrete Mathematics

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.

Keywords

Cite

@article{arxiv.2007.06728,
  title  = {On the Parallel Tower of Hanoi Puzzle: Acyclicity and a Conditional Triangle Inequality},
  author = {Andrey Rukhin},
  journal= {arXiv preprint arXiv:2007.06728},
  year   = {2022}
}

Comments

To be presented at the SIAM Conference on Discrete Mathematics 2022; Updates/Edits to the statement of Theorem 3.2 included