**The study of combinatorics on words, or finite sequences of symbols from a
finite alphabet, finds applications in several areas of biology, computer
science, mathematics, and physics. Molecular biology, in particular, has stimulated considerable
interest
in the study of combinatorics on partial words that are sequences that may have
a
number of “do not know” symbols also called “holes”. This paper is devoted to a
fundamental result on periods of words, the Critical Factorization Theorem,
which states that the period of a word is always locally detectable in at least
one position of the word resulting in a corresponding critical factorization.
Here, we describe precisely the class of partial words w with one hole for which
the weak period is locally detectable in at least one position of w. Our proof
provides an algorithm which computes a critical factorization when one exists.**

**Keywords:** **Word, partial word, period, weak period, local period.**