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Detecting Patterns in Finite Regular and Context-Free Languages

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Executive Summary

The computational complexity of pattern matching has received much attention in the literature. Although determining whether a given word appears inside another can be done in linear time, other pattern-matching problems appear to be computationally intractable. In a classic paper, Angluin showed the problem of determining if an arbitrary pattern matches an arbitrary string is NP-complete. More recently, Anderson et al. showed that pattern matching becomes PSPACE-complete if the authors are trying to match a pattern against words of a language specified by a DFA, NFA, or regular expression.

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