Visibly Rational Expressions

Laura Bozzelli and César Sánchez
Regular Expressions (RE) are an algebraic formalism for expressing regular languages, widely used in string search and as a specification language in verification. In this paper we introduce and investigate Visibly Rational Expressions (VRE), an extension of RE for the well-known class of Visibly Pushdown Languages (VPL). We show that VRE capture the class of VPL. Moreover, we identify an equally expressive fragment of VRE which admits a quadratic time compositional translation into the automata acceptors of VPL. We also prove that, for this fragment, universality, inclusion and language equivalence are EXPTIME-complete. Finally, we provide an extension of VRE for VPL over infinite words.
In IARCS Proceedings of the Annual Conference on Foundations of Software Technology and Theoretical Computer Science, (FSTTCS 2012) December 15-17, 2012, Hyderabad, India.
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