The subword complexity of a language K is the function which to every positive integer n assigns the number of different subwords of length n occurring in words of K. A language K is square-free if no word in it contains a subword of the form xx where x is a nonempty word. The (best) upper and lower bounds on the subword complexity of infinite square-free DOL languages are established.
Ehrenfeucht, Andrzej and Rozenberg, Grzegorz, "On the Subword Complexity of Square-Free DOL Languages ; CU-CS-174-80" (1980). Computer Science Technical Reports. 172.