XML Schema Containment Checking Based on Semi-implicit Techniques
XML schemas are computer languages defining grammars for XML (Extensible Markup Languages) documents. Containment checking for XML schemas has many applications, and is thus important. Since XML schemas are related to the class of tree regular languages, their containment checking is reduced to the language containment problem for non-deterministic tree automata (NTAs). However, an NTA for a practical XML schema has 102−103 states for which the textbook algorithm based on naive determinization is expensive. Thus we in this paper consider techniques based on BDDs (binary decision diagrams). We used semi-implicit encoding which encodes a set of subsets of states as a BDD, rather than encoding a set of states by it. The experiment on several real-world XML schemas proves that our containment checker can answer problems that cannot be solved by previously known algorithms.
KeywordsBoolean Function Binary Tree Regular Expression Binary Decision Diagram Tree Automaton
Unable to display preview. Download preview PDF.
- [BKR97]Morten Biehl, Nils Klarlund, and Theis Rauhe. Algorithms for guided tree automata. In First International Workshop on Implementing Automata, WIA’ 96, London, Ontario, Canada, LNCS 1260. Springer Verlag, 1997.Google Scholar
- [CGP99]Edmund M. Clarke, Jr., Orna Grumberg, and Doron A. Peled. Model Checking. MIT press, 1999.Google Scholar
- [CMS02]Aske Simon Christensen, Anders Muller, and Michael I. Schwartzbach. Static analysis for dynamic XML. In Proceedings of 1st Workshop on Programming Languages Technology for XML (PLAN-X 2002), 2002.Google Scholar
- [HJJ+95]_Jesper G. Henriksen, Jakob L. Jensen, Michael E. Jørgensen, Nils Klarlund, Robert Paige, Theis Rauhe, and Anders Sandholm. Mona: Monadic secondorder logic in practice. In Tools and Algorithms for the Construction and Analysis of Systems, volume 1019 of LNCS, pages 89–110. Springer, 1995.Google Scholar
- [HM02]Haruo Hosoya and Makoto Murata. Validation and boolean operations for attribute-element constraints. In Proceedings of 1st Workshop on Programming Languages Technology for XML (PLAN-X 2002), 2002.Google Scholar
- [HVP00]Haruo Hosoya, Jerome Vouillon, and Benjamin C. Pierce. Regular expression types for XML. In Proceedings of the International Conference on Functional Programming (ICFP), pages 11–22, Sep., 2000.Google Scholar
- [KS01]G.M. Kuper and J. Simeon. Subsumption for XML types. In Proceedings of International Conference on Database Theory (ICDT), Jan., 2001.Google Scholar
- [KSM02]Nils Klarlund, Michael I. Schwartzbach, and Anders Møller. The DSD schema language. Automated Software Engineering Journal, to appear, 2002.Google Scholar
- [MLM01]Makoto Murata, Dongwon Lee, and Murali Mani. Taxonomy of XML schema languages using formal language theory. In Proceedings of Extreme Markup Language 2001, Montreal, pages 153–166, 2001.Google Scholar
- [Ora01]Oraganization for Advancement of Structured Information Standards (OASIS). RELAX NG, 2001. http://www.oasis-open.org/committees/relax-ng/.
- [rel]RELAX (REgular LAnguage description for XML). http://www.xml.gr.jp/relax/.
- [THB95]S. Tasiran, R. Hojati, and R. K. Brayton. Language containment using non-deteministic omega-automata. In Proc. of CHARME’95, volume 987 of LNCS. Springer-Verlag, 1995.Google Scholar
- [Wor00]World Wide Web Consortium. XHTML1.0, 2000. http://www.w3.org/TR/xhtml.