ABSTRACT
We study the satisfiability problem for XPath with data equality tests. XPath is a node selecting language for XML documents whose satisfiability problem is known to be undecidable, even for very simple fragments. However, we show that the satisfiability for XPath with the rightward, leftward and downward reflexive-transitive axes (namely following-sibling-or-self, preceding-sibling-or-self, descendant-or-self) is decidable. Our algorithm yields a complexity of 3EXPSPACE, and we also identify an expressive-equivalent normal form for the logic for which the satisfiability problem is in 2EXPSPACE. These results are in contrast with the undecidability of the satisfiability problem as soon as we replace the reflexive-transitive axes with just transitive (non-reflexive) ones.
- Vince Bárány, Mikołaj Bojańczyk, Diego Figueira, and Paweł Parys. Decidable classes of documents for XPath. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS'12), Leibniz International Proceedings in Informatics (LIPIcs), Hyderabad, India, 2012. Leibniz-Zentrum für Informatik.Google Scholar
- Michael Benedikt, Wenfei Fan, and Floris Geerts. XPath satisfiability in the presence of DTDs. Journal of the ACM, 55(2):1--79, 2008. Google Scholar
Digital Library
- Mikołaj Bojańczyk and Sławomir Lasota. An extension of data automata that captures XPath. In Annual IEEE Symposium on Logic in Computer Science (LICS '10), 2010. Google Scholar
Digital Library
- Mikołaj Bojańczyk, Anca Muscholl, Thomas Schwentick, and Luc Segoufin. Two-variable logic on data trees and XML reasoning. Journal of the ACM, 56(3):1--48, 2009. Google Scholar
Digital Library
- James Clark and Steve DeRose. XML path language (XPath). Website, 1999. W3C Recommendation. http://www.w3.org/TR/xpath.Google Scholar
- Claire David, Leonid Libkin, and Tony Tan. Efficient reasoning about data trees via integer linear programming. ACM Transactions on Database Systems, 37(3):19, 2012. Google Scholar
Digital Library
- Wenfei Fan, Chee Yong Chan, and Minos N. Garofalakis. Secure XML querying with security views. In ACM SIGACT-SIGMOD-SIGART International Conference on Management of Data (SIGMOD'04), pages 587--598. ACM Press, 2004. Google Scholar
Digital Library
- Diego Figueira. Satisfiability of downward XPath with data equality tests. In ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems (PODS'09), pages 197--206. ACM Press, 2009. Google Scholar
Digital Library
- Diego Figueira. Forward-XPath and extended register automata on data-trees. In International Conference on Database Theory (ICDT'10). ACM Press, 2010. Google Scholar
Digital Library
- Diego Figueira. Reasoning on Words and Trees with Data. Phd thesis, Laboratoire Spécification et Vérification, ENS Cachan, France, December 2010.Google Scholar
- Diego Figueira. A decidable two-way logic on data words. In Annual IEEE Symposium on Logic in Computer Science (LICS'11), pages 365--374, Toronto, Canada, 2011. IEEE Computer Society Press. Google Scholar
Digital Library
- Diego Figueira. Alternating register automata on finite data words and trees. Logical Methods in Computer Science, 8(1), 2012.Google Scholar
- Diego Figueira. Decidability of downward XPath. ACM Trans. Comput. Log., 13(4), 2012. Google Scholar
Digital Library
- Diego Figueira and Luc Segoufin. Future-looking logics on data words and trees. In Int. Symp. on Mathematical Foundations of Comp. Sci. (MFCS'09), volume 5734 of LNCS, pages 331--343. Springer, 2009. Google Scholar
Digital Library
- Diego Figueira and Luc Segoufin. Bottom-up automata on data trees and vertical XPath. In International Symposium on Theoretical Aspects of Computer Science (STACS'11), Leibniz International Proceedings in Informatics (LIPIcs). Leibniz-Zentrum für Informatik, 2011.Google Scholar
- Floris Geerts and Wenfei Fan. Satisfiability of XPath queries with sibling axes. In International Symposium on Database Programming Languages (DBPL'05), volume 3774 of Lecture Notes in Computer Science, pages 122--137. Springer, 2005. Google Scholar
Digital Library
- Georg Gottlob, Christoph Koch, and Reinhard Pichler. Efficient algorithms for processing XPath queries. ACM Transactions on Database Systems, 30(2):444--491, 2005. Google Scholar
Digital Library
- Marcin Jurdziński and Ranko Lazić. Alternating automata on data trees and xpath satisfiability. ACM Trans. Comput. Log., 12(3):19, 2011. Google Scholar
Digital Library
- Michael Kaminski and Nissim Francez. Finite-memory automata. Theoretical Computer Science, 134(2):329--363, 1994. Google Scholar
Digital Library
- Michael Kaminski and Tony Tan. Tree automata over infinite alphabets. In Pillars of Computer Science, volume 4800 of Lecture Notes in Computer Science, pages 386--423. Springer, 2008. Google Scholar
Digital Library
- Wim Martens and Frank Neven. Frontiers of tractability for typechecking simple xml transformations. J. Comput. Syst. Sci., 73(3):362--390, 2007. Google Scholar
Digital Library
- Frank Neven, Thomas Schwentick, and Victor Vianu. Finite state machines for strings over infinite alphabets. ACM Trans. Comput. Log., 5(3):403--435, 2004. Google Scholar
Digital Library
- Tony Tan. An automata model for trees with ordered data values. In Annual IEEE Symposium on Logic in Computer Science (LICS'12), pages 586--595. IEEE Computer Society Press, 2012. Google Scholar
Digital Library
Index Terms
On XPath with transitive axes and data tests
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