Operator Precedence and the Visibly Pushdown Property

Abstract

Operator precedence languages, designated as Floyd's Languages (FL) to honor their inventor, are a classical deterministic context-free family. FLs are known to be a boolean family, and have been recently shown to strictly include the Visibly Pushdown Languages (VPDL); the latter are FLs characterized by operator precedence relations determined by the alphabet partition. In this paper we give the non-obvious proves that FLs have the same closure properties that motivated the introduction of VPDLs, namely under reversal, concatenation and Kleene's star. Thus, rather surprisingly, the historical FL family turns out to be the largest known deterministic context-free family that includes the VPDL and has the same closure properties needed for applications to model checking and for defining mark-up languages such as HTML. As a corollary, an extended regular expression of precedence-compatible FLs is a FL and a deterministic parser for it can be algorithmically obtained.