Order Conditions for Languages

Abstract

We define a condition on the resolution of bispecials in a language. A language satisfies this order condition if and only if it is the natural coding of a generalized interval exchange transformation, while the order condition plus some additional ones characterize the codings of various more classical interval exchange transformations. Also, a finite word clusters for the Burrows-Wheeler transform if and only if the language generated by its powers satisfies an order condition.