Logical definability and query languages over ranked and unranked trees

ACM Transactions on Computational Logic

Volumn 8, Issue 2, 2007, Pages

  Benedikt, Michael ^a   Libkin, Leonid ^b,c   Neven, Frank ^d  

^a LUCENT TECHNOLOGIES   (United States)

^b UNIVERSITY OF EDINBURGH   (United Kingdom)

^c UNIVERSITY OF TORONTO   (Canada)

^d HASSELT UNIVERSITY   (Belgium)

Author keywords

Model theory; Query languages; Ranked trees; Tree automata; Unranked trees

Indexed keywords

MODEL THEORY; RANKED TREES; TREE AUTOMATA; UNRANKED TREES;

BINARY SEQUENCES; COMPUTATIONAL COMPLEXITY; CONSTRAINT THEORY; POLYNOMIAL APPROXIMATION; QUERY LANGUAGES; XML;

DECISION TREES;

EID: 34247241155     PISSN: 15293785     EISSN: 1557945X     Source Type: Journal    
DOI: 10.1145/1227839.1227843     Document Type: Article

References (53)

1. ABITEBOUL, S., HULL, R., AND VIANU, V. 1995. Foundations of Databases. Addison-Wesley.
2. AIKEN, A. 1994. Set constraints: Results, applications, and future directions. In PPCP: Proceedings of the 2nd International Workshop on Principles and Practice of Constraint Programming. Lecture Notes in Computer Science, vol. 874. Springer Verlag. 326-335.
3. ANGLUIN, D. AND HOOVER, D. N. 1984. Regular prefix relations. Math. Syst. Theory 17, 3, 167-191.
4. ANTHONY, M. AND BIGGS, N. 1992. Computational Learning Theory. Cambridge University Press.
5. BENEDIKT, M. AND LIBKIN, L. 2000. Relational queries over interpreted structures. J. ACM 47, 4, 644-680.
6. BENEDIKT, M., LIBKIN, L., SCHWENTICK, T., AND SEGOUFIN, L. 2003. Definable relations and first-order query languages over strings. J. ACM 50, 5, 694-751.
7. BLUMENSATH, A. AND GRÄEL, E. 2000. Automatic structures. In LICS: Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science. 51.
8. BÖRGER, E., GRÄDEL, E., AND GUREVICH, Y. 1997. The Classical Decision Problem. Springer Verlag.
9. BRAY, T., PAOLI, J., SPERBERG-MCQUEEN, C. M., AND MALER, E. 2000. Extensible Markup Language (XML) 1.0, 2nd ed. W3C recommendation. http://www.w3.org/XML.
10. BHÜGGEMANN-KLEIN, A., MURATA, M., AND WOOD, D. 2001. Regular tree and regular hedge languages over unranked alphabets: Version 1. Tech. Rep. HKUST-TCSC-2001-0, The Hongkong University of Science and Technology.
11. BRUYÈRE, V., HANSEL, G., MICHAUX, C., AND VILLEMAIRE, R. 1994. Logic and p-recognizable sets of integers. Bull. Belgian Math. Soc. 1, 191-238.
12. CARDELLI, L. AND GHELLI, G. 2004. TQL: A query language for semistructured data based on the ambient logic. Math. Structures Comput. Sci. 14, 3, 285-327.
13. CHAMBERLIN, D., CLARK, J., FLORESCU, D., ROBIE, J., SIMEON, J., AND STEFANASCU, M. 2002. XQuery 1.0: An XML query language. http://www.w3.org/TR/xquery/.
14. CLARK, J. 1999. XSL transformations version 1.0. http://www.w3.org/TR/WD-xslt.
15. CLARK, J. AND DEROSE, S. 1999. XML path language (XPath). http://www.w3.org/TR/xpath.
16. COMON, H., DAUCHET, M., GILLERON, R., JACQUEMARD, F., LUGIEZ, D., TISON, S., AND TOMMASI, M. 1997. Tree automata techniques and applications, http://www.grappa.univ-lille3.fr/tata.
17. DANTSIN, E. AND VORONKOV, A. 2000. Expressive power and data complexity of nonrecursive query languages for lists and trees (extended abstract). In PODS: Proceedings of the 19th ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems. ACM Press, New York. 157-165.
18. DONER, J. 1970. Tree acceptors and some of their applications. J. Comput. Syst. Sci. 4, 406-451.
19. DÖRRE, J. 1991. Feature logic with weak subsumption constraints. In Proceedings of the 29th Annual Meeting on Association for Computational Linguistics. Association for Computational Linguistics, 256-263.
20. EBBINGHAUS, H.-D. AND FLUM, J. 1999. Finite Model Theory, 2nd ed. Springer Verlag.
21. ELGAARD, J., KLARLUND, N., AND MØLLER, A. 1998. Mona 1.x: New techniques for ws1s and ws2s. In CAV: Proceedings of the 10th International Conference on Computer Aided Verification, A. J. Hu and M. Y. Vardi, eds. Lecture Notes in Computer Science, vol. 1427. Springer Verlag. 516-520.
22. ÉSIK, Z. 1998. Axiomatizing the equational theory of regular tree languages (extended anstract). In STAGS: Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science, M. Morvan et al. eds. Lecture Notes in Computer Science, vol. 1373. Springer Verlag. 455-465.
23. FLUM, J. AND ZIEGLER, M. 1999. Pseudo-Finite homogeneity and saturation. J. Symb. Logic 64, 1689-1699.
24. GOTTLOB, G., KOCH, C., PICHLER, R., AND SEGOUFIN, L. 2005. The complexity of Xpath query evaluation and XML typing. J. ACM 52, 2, 284-335.
25. HODGES, W. 1993. Model Theory. Cambridge University Press, New York.
26. HODGSON, B. 1983. Décadabilité par automate fini. Ann. Sci. Math. Québec 7, 39-57.
27. IMMERMAN, N. 1998. Descriptive Complexity. Springer Verlag.
28. KHOUSSAINOV, B. AND NERODE, A. 1995. Automatic presentations of structures. In LCC: Logical and Computational Complexity, D. Leivant, ed. Lecture Notes in Computer Science, vol. 960. Springer Verlag. 367-392.
29. KOLB, H.-P. AND MÖNNICH, U. 1999. The Mathematics of Syntactic Structure: Trees and Their Logics. Walter De Gruyter, Hawthorne, NY.
30. KUPFEEMAN, O., SAFRA, S., AND VABDI, M. Y. 1996. Relating word and tree automata. In LICS: Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science. 322.
31. LASKOWSKI, M. C. 1992. Vapnik-Chervonenkis classes of definable sets. J. London Math. Soc. 45, 377-384.
32. LOHREY, M. 2001. On the parallel complexity of tree automata. In RTA: Proceedings of the 12th International Conference on Rewriting Techniques and Applications, A. Middeldorp, ed. Lecture Notes in Computer Science, vol. 2051. Springer Verlag. 201-215.
33. MARX, M. 2004. Conditional Xpath, the first order complete Xpath dialect. In PODS: Proceedings of the 23rd ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems. ACM Press, New York. 13-22.
34. MÜLLER, M. AND NIEHREN, J. 2000. Ordering constraints over feature trees expressed in second-order monadic logic. Inf. Comput. 159, 1-2, 22-58.
35. MÜLLER, M., NIEHREN, J., AND PODELSKI, A. 2000. Ordering constraints over feature trees. Constraints 5, 1-2, 7-41.
36. MÜLLER, M., NIEHREN, J., AND TREINEN, R. 2001. The first-order theory of ordering constraints over feature trees. Discrete Math. Theor. Comput. Sci. 4, 2, 193-234.
37. NEVEN, P. AND SCHWENTICK, T. 2000. Expressive and efficient pattern languages for tree-structured data (extended abstract). In PODS: Proceedings of the 19th ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems. ACM Press, New York. 145-156.
38. NEVEN, F. AND SCHWENTICK, T. 2002. Query automata on finite trees. Theor. Comput. Sci. 275, 633-674.
39. NIWINSKI, D. AND WALUKIEWICZ, I. 1998. Relating hierarchies of word and tree automata. In STACS: Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science, M. Morvan et al. eds. Lecture Notes in Computer Science, vol. 1373. Springer Verlag. 320-331.
40. POTTHOFF, A. AND THOMAS, W. 1993. Regular tree languages without unary symbols are starfree. In FCT: Proceedings of the 9th International Symposium on Fundamentals of Computation Theory, Z. Ésik, ed. Lecture Notes in Computer Science, vol. 710. Springer Verlag. 396-405.
41. RABIN, M. 1969. Decidability of second-order theories and automata on infinite trees. Trans. Amer. Math. Soci. 141, 1-35.
42. SMOLKA, G. 1995. The OZ programming model (extended abstract). In Euro-Par: Proceedings of the 1st International Euro-Par Conference on Parallel Processing, S. Haridi and P. Magnusson, eds. Lecture Notes in Computer Science, vol. 966. Springer Verlag. 5-8.
43. SMOLKA, G. AND TREINEN, R. 1994. Records for logic programming. J. Logic Program. 18, 229-258.
44. STOLBOUSHKIN, A. AND TAITSLIN, M. 1999. Finite queries do not have effective syntax. Inf. Comput. 153, 99-116.
45. SU, Z., AIKEN, A., NIEHREN, J., PRIESNITZ, T., AND TREINEN, R. 2002. The first-order theory of sub-typing constraints. In POPL: Proceedings of the 29th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages. ACM Press, 203-216.
46. SUCIU, D. 2002. Typechecking for semistructured data. In DBPL: Revised Papers from the 8th International Workshop on Database Programming Languages, G. Ghelli and G. Grahne, eds. Lecture Notes in Computer Science, vol. 2397. Springer Verlag. 1-20.
47. THATCHER, J. AND WRIGHT, J. 1968. Generalized finite automata theory with an application to a decision problem of second-order logic. Math. Syst. Theory 2, 1, 57-81.
48. THOMAS, W. 1984. Logical aspects in the study of tree languages. In Proceedings of the 9th International Colloquium on Trees in Algebra and Programming, B. Courcelle, ed. Cambridge University Press, New York. 31-50.
49. THOMAS, W. 1987. On chain logic, path logic, and first-order logic over infinite trees. In Symposium on Logic in Computer Science. 245-256.
50. THOMAS, W. 1997. Languages, automata, and logic. In Handbook of Formal Languages, vol. 3. G. Rozenberg and A. Salomaa, eds. Springer Verlag. 389-456.
51. VOLLMER, H. 1999. Introduction to Circuit Complexity. Springer Verlag.
52. VOROBYOV, S. AND VORONKOV, A. 1998. Complexity of nonrecursive logic programs with complex values. In PODS: Proceedings of the 17th ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems. ACM Press, New York. 244-253.
53. WILKE, T. 1996. An algebraic characterization of frontier testable tree languages. Theor. Comput. Sci. 154, 1, 85-106.