Every Iterated Morphism Yields a co-CFL

Recently, Main [3] and Main, Bucher and Haussler [4] disproved quite a lot of conjectures about various classes of context-free languages by showing that the complement of the set of left factors of the T h u e M o r s e sequence and of other related infinite words is context-free. The aim of this article is to extend the latter result by showing, with almost the same proof technique, that, for any i terated morphism, the complement of the set of left factors of an infinite word it generates is context-free. It appears in the construction that the language is even one-counter (in the sense of Gre ibach [2]).