TL;DR
This paper explores the properties and characterizations of morphic sequences, extending known closure properties and providing new characterizations based on automata, subsequences, rationality, and rewriting.
Contribution
It extends the understanding of morphic sequences by offering new characterizations and relating them to automata, subsequences, and rewriting systems.
Findings
Morphic sequences have limited known characterizations.
A new characterization based on automata is discussed.
Relation to rationality and infinitary rewriting is established.
Abstract
Morphic sequences form a natural class of infinite sequences, extending the well-studied class of automatic sequences. Where automatic sequences are known to have several equivalent characterizations and the class of automatic sequences is known to have several closure properties, for the class of morphic sequences similar closure properties are known, but only limited equivalent characterizations. In this paper we extend the latter. We discuss a known characterization of morphic sequences based on automata and we give a characterization of morphic sequences by finiteness of a particular class of subsequences. Moreover, we relate morphic sequences to rationality of infinite terms and describe them by infinitary rewriting.
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.
Taxonomy
Topicssemigroups and automata theory · Advanced Algebra and Logic · Logic, programming, and type systems