Visibly Pushdown Transducers for Approximate Validation of Streaming XML

Abstract

Visibly Pushdown Languages (VPLs), recognized by Visibly Pushdown Automata (VPAs), are a nicely behaved family of context-free languages. It has been shown that VPAs are equivalent to Extended Document Type Definitions (EDTDs), and thus, they provide means for elegantly solving various problems on XML. Especially, it has been shown that VPAs are the apt device for streaming XML.One of the important problems about XML that can be addressed using VPAs is the validation problem in which we need to decide whether an XML document conforms to the specification given by an EDTD. In this paper, we are interested in solving the approximate version of this problem, which is to decide whether an XML document can be modified by a tolerable number of edit operations to yield a valid one with respect to a given EDTD.For this, we define Visibly Pushdown Transducers (VPTs) that give us the framework for solving this problem under two different semantics for edit operations on XML. While the first semantics is a generalization of edit operations on strings, the second semantics is new and motivated by the special nature of XML documents. Usings VPTs, we give streaming algorithms that solve the problem under both the semantics. These algorithms use storage space that only depends on the size of the EDTD and the number of tolerable errors. Furthermore, they can check approximate validity of an incoming XML document in a single pass over the document, using auxilliary stack space that is proportional to the depth of the XML document.