Fife's Theorem for (7/3)-Powers
Narad Rampersad (Department of Mathematics, University of Li\`ege),, Jeffrey Shallit (School of Computer Science, University of Waterloo), Arseny, Shur (Department of Algebra, Discrete Mathematics, Ural Federal, University)
TL;DR
This paper characterizes infinite binary (7/3)-power-free words using a finite automaton and identifies which of these words are 2-automatic, advancing understanding of pattern avoidance in infinite sequences.
Contribution
It provides a finite automaton-based characterization of (7/3)-power-free words and identifies 2-automatic instances, offering a new structural perspective.
Findings
Finite automaton with 15 states encodes all (7/3)-power-free words.
Characterization of (7/3)-power-free words that are 2-automatic.
Enhanced understanding of pattern avoidance in infinite binary sequences.
Abstract
We prove a Fife-like characterization of the infinite binary (7/3)-power-free words, by giving a finite automaton of 15 states that encodes all such words. As a consequence, we characterize all such words that are 2-automatic.
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Taxonomy
Topicssemigroups and automata theory · Computability, Logic, AI Algorithms · Logic, programming, and type systems