The Efficiency of Discrete Convolution Method on Solving Exact String Matching Problem

In this paper, we first derived an equation which can approach the probability of appearing of a pattern string in a text string. From this equation, we see that the probability that a pattern string appears in a text string reduces to 0 quickly as the length of the pattern string increases. Because of this observation, we introduce an algorithm based on the discrete convolution method with an early termination. The algorithm stops as soon as it discovers that a prefix of the pattern string does not appear in the text string. In this paper, we show that the discrete convolution method with an early termination is quite efficient to solve exact string matching problem.