On Harrison’s substring testing technique

This note comments on a technique by Malcolm Harrison [1] that tests whether a given string of characters, S1, is a substring of another string of characters, S2. This technique first transforms S2 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 S1 and S2 are decomposed into l1 and l2 segments respectively.

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