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We have proved that for any pattern p the tail recursive program model ofnaive pattern matching may be automatically specialized w.r.t. the pattern p toa specialized version of the so-called KMP-algorithm, using the Higman-Kruskalrelation that controls the unfolding/folding. Given an input string, thecorresponding residual program finds the first occurrence of p in the string inlinear time on the string length. The current state of the automated programspecialization art based on unfolding/folding is too weak in order to be ableto reproduce the proof, done by hands, of the uniform property above, while itknown before that program specialization is sometimes able to produce theKMP-algorithm for a few concrete static patterns.

On Specialization of a Program Model of Naive Pattern Matching in Strings (Extended Abstract)