Efficient Algorithm for Learning Simple Regular Expressions from Noisy Examples

We present an efficient algorithm for finding approximate repetitions in a given sequence of characters. First, we define a class of simple regular expressions which are of star-height one and do not contain union operations, and a stochastic mutation process of a given length over a string of characters. Then, assuming that a given string of characters is obtained corrupted by the defined mutation process from some long enough word generated by a simple regular expression, we try to restore the expression. We prove that to within some reasonable accuracy it is always possible if the length of the mutation process is bounded comparing to the length of the example. We provide an algorithm by which the expression can be restored in linear time in the length of the example and no worse than quadratic in the length of the expression. We discuss some extensions of the method and possible applications to bioinformatics.

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