# Simply modified GKL density classifiers that reach consensus faster

## TL;DR

This paper introduces modified GKL cellular automaton models with extended neighborhoods that classify densities efficiently and reach consensus significantly faster, highlighting the importance of consensus time as a performance metric.

## Contribution

The paper presents new modified GKL models with extended neighborhoods that improve consensus speed while maintaining classification accuracy.

## Key findings

- Modified GKL models reach consensus more than twice as fast.
- Extended neighborhoods do not compromise classification performance.
- Consensus time is a valuable performance measure.

## Abstract

The two-state Gacs-Kurdyumov-Levin (GKL) cellular automaton has been a staple model in the study of complex systems due to its ability to classify binary arrays of symbols according to their initial density. We show that a class of modified GKL models over extended neighborhoods, but still involving only three cells at a time, achieves comparable density classification performance but in some cases reach consensus more than twice as fast. Our results suggest the time to consensus (relative to the length of the CA) as a complementary measure of density classification performance.