Algorithms for Greechie Diagrams

TL;DR

This paper introduces a new, more efficient algorithm for generating Greechie diagrams, improving upon previous methods, and provides tools for verifying their properties within orthomodular lattice varieties.

Contribution

The authors present a novel algorithm for generating Greechie diagrams with arbitrary atoms or blocks, and develop programs for their verification and analysis.

Findings

Previous algorithms do not generate all diagrams.

New algorithm is at least 100,000 times faster.

Tools are provided for checking diagram validity and properties.

Abstract

We give a new algorithm for generating Greechie diagrams with arbitrary chosen number of atoms or blocks (with 2,3,4,... atoms) and provide a computer program for generating the diagrams. The results show that the previous algorithm does not produce every diagram and that it is at least 100,000 times slower. We also provide an algorithm and programs for checking of Greechie diagram passage by equations defining varieties of orthomodular lattices and give examples from Hilbert lattices. At the end we discuss some additional characteristics of Greechie diagrams.