On Harrison's substring testing technique

Abstract

This note comments on a technique by Malcolm Harrison [1] that tests whether a given string of characters, S 1 , is a substring of another string of characters, S 2 . This technique first transforms S 2 into the set consisting of all the smaller fixed size substrings of length k and then hashes each of these segments into the m positions of a computer “word”; the bit corresponding to a position in this word is turned on if at least one segment is hashed onto it; else it is zero. The test is based on the observation that the same procedure applied to an arbitrary substring of the first string will not turn on any new bits. In the following we shall assume that S 1 and S 2 are decomposed into l 1 and l 2 segments respectively.