Efficient asymmetric inclusion of regular expressions with interleaving and counting for XML type-checking

The inclusion of Regular Expressions (REs) is the kernel of any type-checking algorithm for XML manipulation languages. XML applications would benefit from the extension of REs with interleaving and counting, but this is not feasible in general, since inclusion is EXPSPACE-complete for such extended REs. In Colazzo et al. (2009) [1] we introduced a notion of ?conflict-free REs?, which are extended REs with excellent complexity behaviour, including a polynomial inclusion algorithm [1] and linear membership (Ghelli et al., 2008 [2]). Conflict-free REs have interleaving and counting, but the complexity is tamed by the ?conflict-free? limitations, which have been found to be satisfied by the vast majority of the content models published on the Web.However, a type-checking algorithm needs to compare machine-generated subtypes against human-defined supertypes. The conflict-free restriction, while quite harmless for the human-defined supertype, is far too restrictive for the subtype. We show here that the PTIME inclusion algorithm can be actually extended to deal with totally unrestricted REs with counting and interleaving in the subtype position, provided that the supertype is conflict-free.This is exactly the expressive power that we need in order to use subtyping inside type-checking algorithms, and the cost of this generalized algorithm is only quadratic, which is as good as the best algorithm we have for the symmetric case (see [1]). The result is extremely surprising, since we had previously found that symmetric inclusion becomes NP-hard as soon as the candidate subtype is enriched with binary intersection, a generalization that looked much more innocent than what we achieve here

Efficient inclusion for a class of XML types with interleaving and counting

SUMMARY: Inclusion between XML types is important but expensive, and is much more expensive when unordered types are considered. We prove here that inclusion for XML types with interleaving and counting can be decided in polynomial time in the presence of two important restrictions: no element appears twice in the same content model, and Kleene star is only applied to disjunctions of single elements. Our approach is based on the transformation of each such content model into a set of constraints that completely characterizes the generated language. We then reduce inclusion checking to constraint implication. We exhibit a quadratic algorithm to perform inclusion checking on a RAM machine

Distributed XML Design

A distributed XML document is an XML document that spans several machines. We assume that a distribution design of the document tree is given, consisting of an XML kernel-document T[f1,...,fn] where some leaves are "docking points" for external resources providing XML subtrees (f1,...,fn, standing, e.g., for Web services or peers at remote locations). The top-down design problem consists in, given a type (a schema document that may vary from a DTD to a tree automaton) for the distributed document, "propagating" locally this type into a collection of types, that we call typing, while preserving desirable properties. We also consider the bottom-up design which consists in, given a type for each external resource, exhibiting a global type that is enforced by the local types, again with natural desirable properties. In the article, we lay out the fundamentals of a theory of distributed XML design, analyze problems concerning typing issues in this setting, and study their complexity.Comment: "56 pages, 4 figures

Efficient inclusion for a class of XML types with interleaving and counting

Inclusion between XML types is important but expensive, and is much more expensive when unordered types are considered. We prove here that inclusion for XML types with interleaving and counting can be decided in polynomial time in presence of two important restrictions: no element appears twice in the same content model, and Kleene star is only applied to disjunctions of single elements. Our approach is based on the transformation of each such type into a set of constraints that completely characterizes the type. We then provide a complete deduction system to verify whether the constraints of one type imply all the constraints of another one.