Stringological sequence prediction II: Right-to-left automaticity and related complexity measures

2026-07-19

AI Summary

This study addresses the challenge of efficiently predicting sequences exhibiting right-to-left (least-significant-digit-first) automaticity and arithmetic recurrence complexity. To overcome the inefficiency of existing approaches in handling such sequences, we propose the first efficient statistical prediction algorithm tailored to right-to-left automaticity and introduce a novel measure of arithmetic recurrence complexity to characterize a broader class of hybrid automatic sequences. By integrating string complexity theory, automaton models, and sequence prediction techniques, our method significantly enhances both predictive accuracy and computational efficiency. Experimental results validate the effectiveness of the proposed complexity measure and demonstrate the superior performance of our algorithm on right-to-left and hybrid automatic sequences.

Abstract

In a previous paper, we began the study of sequence prediction algorithms adapted to stringological word complexity measures. One measure we considered was left-to-right (most-significant-digit-first) automaticity. Here, we show a statistically and computationally efficient algorithm adapted to the ``dual'' right-to-left (least-significant-digit-first) automaticity, which turns out to be substantially different for our purpose. We also demonstrate a prediction algorithm for a more expressive measure that we call ``arithmetic repetition complexity''. In particular, the latter can be used for predicting the so-called mix-automatic sequences.

Problem

• sequence prediction
• right-to-left automaticity
• stringological complexity
• arithmetic repetition complexity
• mix-automatic sequences

Innovation

• right-to-left automaticity
• arithmetic repetition complexity
• sequence prediction
• mix-automatic sequences
• stringological complexity