Abstract

We consider several open problems of Karhumaki, Mignosi, and Plandowski, cf. [KMP], concerning the expressibility of languages and relations as solutions of word equations. We show first that the (scattered) subword relation is not expressible. Then, we consider the set of k-power free finite words and solve it negativelly for all nontrivial integer values of k. Finally, we consider the Fibonacci finite words. We do not solve the problem of the expressibility of the set of these words but prove that it cannot be given a negative answer (as believed) using the tools in [KMP]. 1

Citations