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

Dario Colazzo 1, 2 Giorgio Ghelli 3 Luca Pardini 4 Carlo Sartiani 5
1 OAK - Database optimizations and architectures for complex large data
CNRS - Centre National de la Recherche Scientifique : UMR8623, Inria Saclay - Ile de France, UP11 - Université Paris-Sud - Paris 11, LRI - Laboratoire de Recherche en Informatique
Abstract : 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.
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Article dans une revue
Theoretical Computer Science, Elsevier, 2013
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https://hal.inria.fr/hal-00923688
Contributeur : Dario Colazzo <>
Soumis le : vendredi 3 janvier 2014 - 19:29:49
Dernière modification le : lundi 28 mai 2018 - 14:38:02

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Dario Colazzo, Giorgio Ghelli, Luca Pardini, Carlo Sartiani. Efficient asymmetric inclusion of regular expressions with interleaving and counting for XML type-checking. Theoretical Computer Science, Elsevier, 2013. 〈hal-00923688〉

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