Let w be an infinite word generated (by iteration) by a given morphism. Let p be any rational number. If there exists a word u such that u^p is a factor of w, then p is an exponent of w. The exponent of a morphism generating w is the supremum of the exponents of w. Given a morphism α and a number t, is it decidable whether t is an exponent of α?

This is known to be decidable in the case where the morphism is k-uniform for any integer k ≥ 2.

-- JeffreyShallit - 13 Jul 2011