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 work we investigate Visibly Rational Expressions (VRE), an extension of RE for the well-known class of Visibly Pushdown Languages (VPL), a particularly well-behaved class of context free languages.

I will, on demand and in an informal style, show some of the most relevant results:

• VRE capture precisely the class of VPL.
• An equally expressive fragment of VRE, which admits a quadratic time translation into the automata acceptors of VPL.
• For this fragment, universality, inclusion and language equivalence are EXPTIME-complete.
• An extension of dVRE for VPL over infinite words.
• On-going work about fusing VRE and RLTL into a temporal logic for nested word languages.

This is joint work with Laura Bozzelli.