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The pattern matching problem is to find all occurrences of patterns in a text string. An extended problem is considered for patterns with pictures, where a picture is a don't-care that matches only th...e symbols in the set it represents. For example, let $ A $ be a picture $ a, b, ldots , z $, and $ N $ for $ 0, 1, ldots , 9 $. Then, $ mathrm{ab}NN $, $ mathrm{a7}NNNNA, ldots $ are patterns. For multiple string patterns, the Aho-Corasick algorithm, which uses a finite state pattern matching machine, is widely known to be quite efficient. A fast matching algorithm for multiple patterns with pictures is presented as a natural extension of the AC algorithm. A pattern matching machine can be built easily, and then it runs in linear time proportional to the text length as the AC algorithm achieves. Moreover, a correctness proof of the algorithm is given.show more
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