  The critical exponent of an infinite word is defined to be the supremum of
the exponent of each of its factors. For k-automatic sequences, we show that
this critical exponent is always either a rational number or infinite, and its
value is computable. Our results also apply to variants of the critical
exponent, such as the initial critical exponent of Berthe, Holton, and Zamboni
and the Diophantine exponent of Adamczewski and Bugeaud. Our work generalizes
or recovers previous results of Krieger and others, and is applicable to other
situations; e.g., the computation of the optimal recurrence constant for a
linearly recurrent k-automatic sequence.
