String-matching with OBDDs

Ordered binary decision diagrams (OBDDs) are a very popular graph representation for Boolean functions. They can be viewed as finite automata recognizing sets of strings of a fixed length, where the letters of the input strings are read at most once in a predefined ordering. The string matching problem with string w as pattern, consists of determining, given an input string, whether or not it contains w as substring. We show that for a fraction of orderings tending to 1 when n increases arbitrarily, the minimal size of an OBDD solving the string matching problem for strings of length n has a growth which is an exponential in n.