Regular Expressions and Predicate Logic in Finite-State Language Processing

This paper proposes an extension to the formalism of regular expressions with a form of predicate logic where quantified propositions apply to substrings. The implementation hinges crucially on the manipulation of auxiliary symbols which has been a common, though previously unsystematized practice in finite-state language processing. We also apply the notation to give alternate compilation methods for two-level grammars and various types of replacement rules found in the literature, and show that, under a certain interpretation, two-level rules and many types of replacement rules are equivalent.