Relationally Periodic Sequences and Subword Complexity

By the famous theorem of Morse and Hedlund, a word is ultimately periodic if and only if it has bounded subword complexity, i.e., for sufficiently large n, the number of factors of length n is constant. In this paper we consider relational periods and relationally periodic sequences, where the relation is a similarity relation on words induced by a compatibility relation on letters. We investigate what would be a suitable definition for a relational subword complexity function such that it would imply a Morse and Hedlund-like theorem for relationally periodic words. We consider strong and weak relational periods and two candidates for subword complexity functions. Key words: Period, subword complexity, similarity relation, relational period, partial word

• Type: Conference
• Year: 2008
• Where: DLT
• Authors: Julien Cassaigne, Tomi Kärki, Luca Q. Zamboni
• Keywords: DLT 2008, Relational Period, Subword Complexity, Subword Complexity Functions, Theoretical Computer Science