A Space Efficient Algorithm for the Calculation of the Digit Distribution in the Kolakoski Sequence

TL;DR

This paper introduces a space-efficient linear-time algorithm for calculating digit distributions in the classical Kolakoski sequence, which can be adapted to generalized sequences, improving computational feasibility.

Contribution

The authors develop a logarithmic space algorithm for digit distribution calculation in the Kolakoski sequence, enhancing efficiency over standard methods.

Findings

Algorithm runs in linear time with logarithmic space complexity.

Easily adaptable to generalized Kolakoski sequences.

Significantly reduces memory requirements for sequence analysis.

Abstract

With standard algorithms for generating the classical Kolakoski sequence, the numerical calculation of the digit distribution requires a linear amount of space. Here, we present an algorithm for calculating the distribution of the digits in the classical Kolakoski sequence, that only requires a logarithmic amount of space and still runs in linear time. The algorithm is easily adaptable to generalised Kolakoski sequences.