Circularly Squarefree Words and Unbordered Conjugates: A New Approach.

Using a new approach based on automatic sequences, logic, and a decision procedure, we reprove some old theorems about circularly squarefree words and unbordered conjugates in a new and simpler way. Furthermore, we prove two new results about unbordered conjugates: we complete the classification, due to Harju and Nowotka, of binary words with the maximum number of unbordered conjugates, and we prove that for every possible number, up to the maximum, there exists a word having that number of unbordered conjugates.