Augmented regular expressions: a formalism to describe, recognize, and learn a class of context-sensitive languages

Abstract

In order to extend the potential of application of the syntactic approach to pattern recognition, the efficient use of models capable of describing context-sensitive structural relationships is needed. Moreover, the ability to learn such models from examples is interesting to automate as much as possible the development of applications. In this paper, a new formalism that permits to describe a non-trivial class of context-sensitive languages, the Augmented Regular Expressions (AREs), is introduced. AREs augment the descriptive power of regular expressions by including a set of constraints that involve the number of instances of the operands of the star operations in each string of the language. Likewise, algorithms are given to infer AREs from string examples and to recognize language strings by AREs. The method for learning AREs consists of a regular grammatical inference step, aimed at obtaining a regular superset of the target language, followed by a constraint induction process, which reduces the extension of the inferred language transforming it into a context-sensitive one. Hence, this two-step approach avoids the difficulty of learning context-sensitive grammars directly from the data. The method for recognizing language strings is also splitted in two stages: matching the underlying regular expression and checking that the resulting star instances satisfy the constraints.