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Efficient asymmetric inclusion between regular expression types

Authors:

Dario Colazzo,

Giorgio Ghelli,

Carlo SartianiAuthors Info & Claims

ICDT '09: Proceedings of the 12th International Conference on Database Theory

Pages 174 - 182

https://doi.org/10.1145/1514894.1514916

Published: 23 March 2009 Publication History

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Abstract

The inclusion of Regular Expressions (REs) is the kernel of any subtype checking algorithm for XML schema 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 [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.

However, the most important use of subtype checking is in the context of type-cheching of XML manipulation languges. A type checker works by testing the inclusion of inferred subtypes in declared supertypes. The conflict-free restriction, while quite harmless for the human-defined supertype, is far too restrictive for the inferred subtype, whose shape is difficult to constrain.

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 [5]). The result is extremely surprising, since we had previously found that asymmetric 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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Cited By

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Chen HZhiwu X(2020)Inclusion algorithms for one-unambiguous regular expressions and their applicationsScience of Computer Programming10.1016/j.scico.2020.102436(102436)Online publication date: Mar-2020
https://doi.org/10.1016/j.scico.2020.102436
Colazzo DGhelli GSartiani C(2017)Linear Time Membership in a Class of Regular Expressions with Counting, Interleaving, and Unordered ConcatenationACM Transactions on Database Systems10.1145/313270142:4(1-44)Online publication date: 13-Nov-2017
https://dl.acm.org/doi/10.1145/3132701
Colazzo DGhelli GPardini LSartiani C(2013)Almost-linear inclusion for XML regular expression typesACM Transactions on Database Systems (TODS)10.1145/2508020.250802238:3(1-45)Online publication date: 5-Sep-2013
https://dl.acm.org/doi/10.1145/2508020.2508022
Show More Cited By

Index Terms

Efficient asymmetric inclusion between regular expression types
1. Information systems
  1. Data management systems
    1. Database design and models
    2. Query languages
2. Theory of computation
  1. Theory and algorithms for application domains
    1. Database theory
      1. Database query languages (principles)

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Type inclusion is a fundamental operation in every type-checking compiler, but it is quite expensive for XML manipulation languages. We recently presented an inclusion checking algorithm for an expressive family of XML type languages which is polynomial,...

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ICDT '09: Proceedings of the 12th International Conference on Database Theory

March 2009

334 pages

ISBN:9781605584232

DOI:10.1145/1514894

Editor:
Ronald Fagin
IBM Research

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Published: 23 March 2009

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EDBT/ICDT '09: EDBT/ICDT '09 joint conference

March 23 - 25, 2009

St. Petersburg, Russia

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Chen HZhiwu X(2020)Inclusion algorithms for one-unambiguous regular expressions and their applicationsScience of Computer Programming10.1016/j.scico.2020.102436(102436)Online publication date: Mar-2020
https://doi.org/10.1016/j.scico.2020.102436
Colazzo DGhelli GSartiani C(2017)Linear Time Membership in a Class of Regular Expressions with Counting, Interleaving, and Unordered ConcatenationACM Transactions on Database Systems10.1145/313270142:4(1-44)Online publication date: 13-Nov-2017
https://dl.acm.org/doi/10.1145/3132701
Colazzo DGhelli GPardini LSartiani C(2013)Almost-linear inclusion for XML regular expression typesACM Transactions on Database Systems (TODS)10.1145/2508020.250802238:3(1-45)Online publication date: 5-Sep-2013
https://dl.acm.org/doi/10.1145/2508020.2508022
Losemann KMartens W(2013)The complexity of regular expressions and property paths in SPARQLACM Transactions on Database Systems10.1145/249452938:4(1-39)Online publication date: 4-Dec-2013
https://dl.acm.org/doi/10.1145/2494529
Losemann KMartens WLenzerini MBenedikt M(2012)The complexity of evaluating path expressions in SPARQLProceedings of the 31st ACM SIGMOD-SIGACT-SIGAI symposium on Principles of Database Systems10.1145/2213556.2213573(101-112)Online publication date: 21-May-2012
https://dl.acm.org/doi/10.1145/2213556.2213573
Amavi JChabin JRéty P(2012)Weak inclusion for recursive XML typesProceedings of the 17th international conference on Implementation and Application of Automata10.1007/978-3-642-31606-7_7(78-89)Online publication date: 17-Jul-2012
https://dl.acm.org/doi/10.1007/978-3-642-31606-7_7
Amavi JChabin JFerrari MRéty P(2011)Weak inclusion for XML typesProceedings of the 16th international conference on Implementation and application of automata10.5555/2032366.2032372(30-41)Online publication date: 13-Jul-2011
https://dl.acm.org/doi/10.5555/2032366.2032372
Colazzo DSartiani CSchneider-Kamp PHanus M(2011)Precision and complexity of XQuery type inferenceProceedings of the 13th international ACM SIGPLAN symposium on Principles and practices of declarative programming10.1145/2003476.2003490(89-100)Online publication date: 20-Jul-2011
https://dl.acm.org/doi/10.1145/2003476.2003490
Colazzo DGhelli GSartiani C(2011)Schemas for safe and efficient XML processingProceedings of the 2011 IEEE 27th International Conference on Data Engineering10.1109/ICDE.2011.5767960(1378-1379)Online publication date: 11-Apr-2011
https://dl.acm.org/doi/10.1109/ICDE.2011.5767960
Amavi JChabin JHalfeld Ferrari MRéty P(2011)Weak Inclusion for XML TypesImplementation and Application of Automata10.1007/978-3-642-22256-6_4(30-41)Online publication date: 2011
https://doi.org/10.1007/978-3-642-22256-6_4
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Almost-linear inclusion for XML regular expression types

Regular expression types for XML

Linear inclusion for XML regular expression types

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