Efficient Inclusion for a Class of XML Types with Interleaving and Counting

Abstract

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 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.

Linear time membership in a class of regular expressions with interleaving and counting

“…The following theorem is proved in [10] and states that constraints provide a sound and complete characterization of type semantics. Theorem 2.14 Given a conflict-free type T , it holds that:…”

“…We show how this approach can be generalized to check membership of XML trees into a class of EDTDs with interleaving and counting, obtaining an algorithm whose time complexity is linear in the product of the input size with the maximal alternation depth of all the content models in the schema. In this context, the restriction we are proposing is known to be met by the vast majority of schemas that are produced in practice [10].…”

“…Our approach is based on the translation of each regular expression into a set of constraints, as in [10]. We define a linear-time translation algorithm, and we then define a linear-time algorithm to check that a word satisfies the resulting constraints.…”

Efficient asymmetric inclusion between regular expression types

“…This fact raised new interest in the study of such extended REs, and, specifically, in the crucial problem of language inclusion. The problem is EXPSPACE-complete [12,8], but, in [9], we introduced a class of "conflict-free" REs with interleaving and counting, whose inclusion problem is in PTIME. The class is characterized by the single occurrence of each symbol and the limitation of Kleene-star to symbols.…”

“…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 [9] we introduced a notion of "conflict-free REs", which are extended REs with excellent complexity behaviour, including a cubic inclusion algorithm [9] and linear membership [10]. 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.…”