Abstract
Motivated by reasoning tasks for XML languages, the satisfiability problem of logics on data trees is investigated. The nodes of a data tree have a label from a finite set and a data value from a possibly infinite set. It is shown that satisfiability for two-variable first-order logic is decidable if the tree structure can be accessed only through the child and the next sibling predicates and the access to data values is restricted to equality tests. From this main result, decidability of satisfiability and containment for a data-aware fragment of XPath and of the implication problem for unary key and inclusion constraints is concluded.
- Alon, N., Milo, T., Neven, F., Suciu, D., and Vianu, V. 2003. XML with data values: Typechecking revisited. J. Comp. Syst. Sci. 66, 4, 688--727. Google ScholarDigital Library
- Arenas, M., Fan, W., and Libkin, L. 2005. Consistency of XML specifications. In Inconsistency Tolerance. Lecture Notes in Computer Science, vol. 3300. Springer-Verlag, New York, pp. 15--41. Google ScholarDigital Library
- Benedikt, M., and Koch, C. 2009. XPath leashed. ACM Comp. Surveys, to appear. Google ScholarDigital Library
- Benedikt, M., Fan, W., and Geerts, F. 2005. XPath satisfiability in the presence of DTDs. In Proceedings of the 24th ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems (PODS'05). ACM, New York, 25--36. Google ScholarDigital Library
- Bojańczyk, M., David, C., Muscholl, A., Schwentick, T., and Segoufin, L. 2006. Two-variable logic on words with data. In Proceedings of the Symposium on Logic in Computer Science (LICS'06). IEEE Computer Society Press, Los Alamitos, CA, 7--16. Google ScholarDigital Library
- Bouyer, P., Petit, A., and Thérien, D. 2003. An algebraic approach to data languages and timed languages. Inf. Comput. 182, 2, 137--162. Google ScholarDigital Library
- Brüggemann-Klein, A., Wood, D., and Murata, M. 2001. Regular tree and regular hedge languages over unranked alphabets. Technical report, April. http://citeseer.ist.psu.edu/451005.html.Google Scholar
- Buneman, P., Davidson, S. B., Fan, W., Hara, C. S., and Tan, W. C. 2003. Reasoning about keys for XML. Inf. Syst. 28, 8, 1037--1063. Google ScholarDigital Library
- Carme, J., Niehren, J., and Tommasi, M. 2004. Querying unranked trees with stepwise tree automata. In RTA'04. Lecture Notes in Computer Science, vol. 3091. Springer-Verlag, New York, 105--118.Google Scholar
- Cristau, J., Löding, C., and Thomas, W. 2005. Deterministic automata on unranked trees. In FCT'05. Lecture Notes in Computer Science, vol. 3623. Springer-Verlag, New York, pp. 68--79. Google ScholarDigital Library
- David, C. 2004. Mots et données infinis. Master thesis, Université Paris 7, LIAFA.Google Scholar
- de Groote, P., Guillaume, B., and Salvati, S. 2004. Vector addition tree automata. In Proceedings of the Symposium on Logic in Computer Science (LICS'04). IEEE Computer Society Press, Los Alamitos, CA, 64--73. Google ScholarDigital Library
- Demri, S., Lazić, R., and Nowak, D. 2005. On the freeze quantifier in constraint LTL: Decidability and complexity. In TIME'05. IEEE Computer Society Press, Los Alamitos, CA, 113--121. Google ScholarDigital Library
- Demri, S., and Lazić, R. 2006. LTL with the freeze quantifier and register automata. In Proceedings of the Symposium on Logic in Computer Science (LICS'06). IEEE Computer Society Press, Los Alamitos, CA, 17--26. Google ScholarDigital Library
- Etessami, K., Vardi, M. Y., and Wilke, Th. 2002. First-order logic with two variables and unary temporal logic. Inf. Comput. 179, 2, 279--295. Google ScholarDigital Library
- Fan, W., and Libkin, L. 2002. On XML integrity constraints in the presence of DTDs. J. ACM. 49, 368--406. Google ScholarDigital Library
- Geerts, F., and Fan, W. 2005. Satisfiability of XPath queries with sibling axes. In DBPL'05. Lecture Notes in Computer Science, vol. 3774. Springer-Verlag, New York, 122--137. Google ScholarDigital Library
- Gottlob, G., Koch, C., and Pichler, R. 2002. Efficient algorithms for processing XPath queries. In Proceedings of the Symposium on Very Large Data Bases (VLDB'02). San Francisco, CA, 95--106. Google ScholarDigital Library
- Grädel, E., and Otto, M. 1999. On logics with two variables. Theoret. Comput. Sci. 224, 73--113. Google ScholarDigital Library
- Jurdziński, M., and Lazić, R. 2007. Alternation-free modal mu-calculus for data trees. In Proceedings of the Symposium on Logic in Computer Science (LICS'07). IEEE Computer Society Press, Los Alamitos, CA, 131--140. Google ScholarDigital Library
- Kaminski, M., and Francez, N. 1994. Finite memory automata. Theoret. Comput. Sci. 134, 2, 329--363. Google ScholarDigital Library
- Kieroński, E., and Otto, M. 2005. Small substructures and decidability issues for first-order logic with two variables. In Proceedings of the Symposium on Logic in Computer Science (LICS'05). IEEE Computer Society Press, Los Alamitos, CA, 448--457. Google ScholarDigital Library
- Martens, W., and Niehren, J. 2005. Minimizing tree automata for unranked trees. In Proceedings of the International Symposium on Database Programming Languages. Lecture Notes in Computer Science, vol. 3774. Springer-Verlag, New York, 232--246. Google ScholarDigital Library
- Marx, M. 2005. First order paths in ordered trees. In ICDT'05. Lecture Notes in Computer Science, vol. 3363. Springer-Verlag, Berlin, Germany, 114--128. Google ScholarDigital Library
- Mortimer, M. 1975. On languages with two variables. Zeitschr. f. math. Logik u. Grundlagen d. Math. 21, 135--140.Google Scholar
- Neven, F., and Schwentick, T. 2003. XPath containment in the presence of disjunction, DTDs, and variables. In ICDT'03, Lecture Notes in Computer Science, vol. 2572. Springer-Verlag, Berlin, Germany, 315--329. Google ScholarDigital Library
- Neven, F., and Schwentick, T. 2002. Query automata. Theoret. Comput. Sci. 275, 1--2, 633--674. Google ScholarDigital Library
- Neeraj Verma, K., Seidl, H., and Schwentick, T. 2005. On the complexity of equational horn clauses. In CADE'05, Lecture Notes in Computer Science, vol. 3632. Springer-Verlag, Berlin, Germany, 337--352. Google ScholarDigital Library
- Neven, F., Schwentick, T., and Vianu, V. 2004. Finite state machines for strings over infinite alphabets. ACM Trans. Comput. Log. 15, 3, 403--435. Google ScholarDigital Library
- Papadimitriou, C. H. 1981. On the complexity of integer programming. J. ACM, 28, 4, 765--768. Google ScholarDigital Library
- XML Path Language (XPath), W3C Recommendation 16 November 1999. Available at http://www.w3.org/TR/xpath.Google Scholar
Index Terms
- Two-variable logic on data trees and XML reasoning
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Two-variable logic on data trees and XML reasoning
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