Direct definition of a ternary infinite square-free sequence
Tetsuo Kurosaki

TL;DR
This paper introduces a new ternary infinite square-free sequence, defined by an iterative process and a finite automaton, extending the concept of automatic sequences like Thue-Morse.
Contribution
It presents a novel ternary square-free sequence with both iterative and automaton-based direct definitions, expanding the class of automatic sequences.
Findings
Sequence is infinite and square-free.
Sequence is generated by a finite automaton.
Sequence is analogous to Thue-Morse in structure.
Abstract
We propose a new ternary infinite (even full-infinite) square-free sequence. The sequence is defined both by an iterative method and by a direct definition. Both definitions are analogous to those of the Thue-Morse sequence. The direct definition is given by a deterministic finite automaton with output. In short, the sequence is automatic.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
