Modeling Repeats in DNA Using Probabilistic Extended Regular Expressions

Regular expressions is a familiar and widely used formalism which is integrated in many modern programming languages. Contemporary versions of regular expressions are typically extended variants whose expressive power goes beyond regular languages. Extended regular expressions are inherently non-deterministic and require procedural control such as backtracking. We propose a probabilistic version of extended regular expressions, where the affinity for strings and matches can be learned from examples. The procedural control semantics are replaced by a probabilistic semantics, where the possible matches are ranked by their probability and the most probable match is the one returned. In the present paper, we show how probabilistic extended regular expressions can be used to model repeats in DNA. To deal with cases where the expressive power of probabilistic extended regular expressions is insufficient, we extend the syntax to integrate external functions, which may be deterministic or probabilistic.