# Algorithmic classification of noncorrelated binary pattern sequences

## TL;DR

This paper presents an algorithm to verify noncorrelation in binary pattern sequences, computes the number of such sequences up to length 4, and proposes a conjecture with partial verification for longer sequences.

## Contribution

It introduces an algorithmic method for verifying noncorrelation and provides exact counts for sequences of certain lengths, along with a new sufficient condition for specific pattern classes.

## Key findings

- Exactly 2272 noncorrelated sequences of length ≤ 4
- A sufficient condition for noncorrelation when patterns do not end with 0
- Conjecture on the necessity of the condition verified for lengths ≤ 5

## Abstract

We show that it is possible to algorithmically verify if a given pattern sequence is noncorrelated. As an application, we compute that there are exactly $2272$ noncorrelated binary pattern sequences of length $\leq 4$. If we restrict our attention to patterns that do not end with $\mathtt{0}$, we put forward a sufficient condition for a pattern sequence to be noncorrelated. We conjecture that this condition is also necessary, and verify this conjecture for lengths $\leq 5$.