String-matching and Other Products

Abstract

The string-matching problem considered here is to find all occurrences of a given pattern as a substring of another longer string. When the pattern is simply a given string of symbols, there is an algorithm due to Morris, Knuth and Pratt which has a running time proportional to the total length of the pattern and long string together. This time may be achieved even on a Turing machine. The more difficult case where either string may have "don't care" symbols which are deemed to match with all symbols is also considered. By exploiting the formal similarity of string-matching with integer multiplication, a new algorithm has been obtained with a running time which is only slightly worse than linear.