[33] Investigate related problems as in Exercise 1.9.6 by replacing finite-state machines (that is, regular languages) by slightly more complex languages such as deterministic one-counter languages or linear languages. Show that there are languages of both types such that selection according to them does not preserve normality (∞-distributedness), and that in fact, for both types of languages it is possible to select a constant sequence from a normal one.

Comments. Source: [W. Merkle, J. Reimann, Theor. Comput. Systems, 39(2006), 685–697].