A Short Note on Improved Logic Circuits in a Hexagonal Minesweeper

TL;DR

This paper enhances the complexity proof of Hexagonal Minesweeper by introducing improved logic circuit configurations, including new gate designs, to better demonstrate its computational hardness.

Contribution

It presents new logic circuit designs for hexagonal Minesweeper, strengthening the PP-hardness proof with clearer signal distinction and innovative circuit components.

Findings

New logic circuit designs for hexagonal Minesweeper

Enhanced proof of PP-hardness using improved circuits

Introduction of novel logic gates and wire configurations

Abstract

This paper aims to present an advanced version of PP-hardness proof of Minesweeper by Bondt. The advancement includes improved Minesweeper configurations for 'logic circuits' in a hexagonal Minesweeper. To do so, I demonstrate logical uncertainty in Minesweeper, which ironically allows a possibility to make some Boolean operators. The fact that existing hexagonal logic circuits did not clearly distinguish the true and false signal needs an improved form of a hexagonal wire. I introduce new forms of logic circuits such as NOT, AND, OR gates, a curve and a splitter of wires. Moreover, these new logic circuits complement Bondt's proof for PP-hardness of Minesweeper by giving a new figure.