Counting interval sizes in the poset of monotone Boolean functions

TL;DR

This paper introduces a resource-efficient algorithm to compute interval sizes in the poset of monotone Boolean functions, successfully applied to the case of seven variables.

Contribution

It presents a novel resource-aware algorithm for counting interval sizes in the poset of monotone Boolean functions, extending computational capabilities.

Findings

Successfully computed interval sizes in D_7

Demonstrated efficiency of the resource-aware algorithm

Extended computational limits for monotone Boolean functions

Abstract

We focus on the computational aspects of counting interval sizes in the poset $D_n$, which represents all monotone Boolean functions of $n$ variables. We present a resource-aware algorithm enabling the calculation of interval sizes in $D_7$.