  In the paper, we investigate two problems on strings. The first one is the
String matching problem, and the second one is the String comparing problem. We
provide a quantum algorithm for the String matching problem that uses
exponentially less quantum memory than existing ones. The algorithm uses the
hashing technique for string matching, quantum parallelism, and ideas of
Grover's search algorithm. Using the same ideas, we provide two algorithms for
the String comparing problem. These algorithms also use exponentially less
quantum memory than existing ones. Additionally, the second algorithm works
exponentially faster than the existing one.
