  Countless variants of the Lempel-Ziv compression are widely used in many
real-life applications. This paper is concerned with a natural modification of
the classical pattern matching problem inspired by the popularity of such
compression methods: given an uncompressed pattern s[1..m] and a Lempel-Ziv
representation of a string t[1..N], does s occur in t? Farach and Thorup gave a
randomized O(nlog^2(N/n)+m) time solution for this problem, where n is the size
of the compressed representation of t. We improve their result by developing a
faster and fully deterministic O(nlog(N/n)+m) time algorithm with the same
space complexity. Note that for highly compressible texts, log(N/n) might be of
order n, so for such inputs the improvement is very significant. A (tiny)
fragment of our method can be used to give an asymptotically optimal solution
for the substring hashing problem considered by Farach and Muthukrishnan.
