  We study here the so called subsequence pattern matching also known as hidden
pattern matching in which one searches for a given pattern $w$ of length $m$ as
a subsequence in a random text of length $n$. The quantity of interest is the
number of occurrences of $w$ as a subsequence (i.e., occurring in not
necessarily consecutive text locations). This problem finds many applications
from intrusion detection, to trace reconstruction, to deletion channel, and to
DNA-based storage systems. In all of these applications, the pattern $w$ is of
variable length. To the best of our knowledge this problem was only tackled for
a fixed length $m=O(1)$ [Flajolet, Szpankowski and Vall\'ee, 2006]. In our main
result we prove that for $m=o(n^{1/3})$ the number of subsequence occurrences
is normally distributed. In addition, we show that under some constraints on
the structure of $w$ the asymptotic normality can be extended to
$m=o(\sqrt{n})$. For a special pattern $w$ consisting of the same symbol, we
indicate that for $m=o(n)$ the distribution of number of subsequences is either
asymptotically normal or asymptotically log normal. We conjecture that this
dichotomy is true for all patterns. We use Hoeffding's projection method for
$U$-statistics to prove our findings.
