Stringological sequence prediction I: efficient algorithms for predicting highly repetitive sequences

2026-03-27

AI Summary

This work addresses the challenge of efficiently predicting highly repetitive structured sequences—such as automatic sequences, morphic sequences, and Sturmian words—by introducing a novel stringology-based framework. The proposed approach pioneers the integration of string complexity measures, including minimal program size and minimal automaton state count, into sequence prediction. It models the sequence generation process using straight-line programs and leverages minimal automata that read k-ary positional inputs to achieve low time and space complexity. Theoretical analysis establishes rigorous error bounds directly tied to the string complexity of the target sequence. Empirical evaluations demonstrate that the algorithm achieves high prediction accuracy across multiple classes of classical low-complexity sequences while offering strong theoretical guarantees.

Technology Category

• Machine Learning: Structured Learning
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We propose novel algorithms for sequence prediction based on ideas from stringology. These algorithms are time and space efficient and satisfy mistake bounds related to particular stringological complexity measures of the sequence. In this work (the first in a series) we focus on two such measures: (i) the size of the smallest straight-line program that produces the sequence, and (ii) the number of states in the minimal automaton that can compute any symbol in the sequence when given its position in base k as input. These measures are interesting because multiple rich classes of sequences studied in combinatorics of words (automatic sequences, morphic sequences, Sturmian words) have low complexity and hence high predictability in this sense.

Problem

• sequence prediction
• stringology
• repetitive sequences
• complexity measures
• automatic sequences

Innovation

• stringology
• sequence prediction
• straight-line program
• automatic sequences
• minimal automaton