Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-06T05:28:32.417Z Has data issue: false hasContentIssue false
  • English
  • Français

On Core XPath with Inflationary Fixed Points∗

Published online by Cambridge University Press:  19 December 2012

Loredana Afanasiev  and
Balder ten Cate
Loredana Afanasiev
Affiliation:
Google Inc., 1600 Amphitheatre Parkway, Mountain View, CA 94043, USA. [email protected]
Balder ten Cate
Affiliation:
Department of Computer Science, University of California at Santa Cruz, 1156 High Street, Santa Cruz, CA 95064, USA.; [email protected]
Get access

Abstract

We prove the undecidability of Core XPath 1.0 (CXP) [G. Gottlob and C. Koch,inProc. of 17th Ann. IEEE Symp. on Logic in Computer Science,LICS ’02(Copenhagen,July 2002). IEEE CS Press (2002) 189–202.] extended with anInflationary Fixed Point (IFP) operator. More specifically,we provethat the satisfiability problem of this language is undecidable. In fact,the fragment ofCXP+IFP containing only the self and descendant axes is already undecidable.

Keywords

Modal Logicfixed pointsXML DatabasesXPath
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 47 , Issue 1: 6th Workshop on Fixed Points in Computer Science (FICS'09) , January 2013 , pp. 3 - 23
Copyright
© EDP Sciences 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

L. Afanasiev, T. Grust, M.J. Marx, J. Rittinger and J. Teubner, An inflationary fixed point operator in XQuery, in Proc. of 24th Int. Conf. on Data Engineering, ICDE ’08 (Cancun, Apr. 2008). IEEE CS Press (2008) 1504–1506.
L. Afanasiev, T. Grust, M.J. Marx, J. Rittinger and J. Teubner, Recursion in XQuery: Put your distributivity safety belt on, in Proc. of 12th Int. Conf. on Extending Database Technology, EDBT ’09 (St. Petersburg, March 2009). ACM Press (2009) 345–356.
P. Blackburn, M. de Rijke and Y. Venema, Modal Logic, Cambridge Tracts in Theoretical Computer Science, Cambridge University Press 53 (2002).
P. Boncz, T. Grust, M. van Keulen, S. Manegold, J. Rittinger and J. Teuber, MonetDB/XQuery: a fast XQuery processor powered by a relational engine, in Proc. of 25th ACM SIGMOD Int. Conf. on Management of Data, SIGMOD ’06 (Chicago, IL, June 2006). ACM Press (2006) 479–490. CrossRef
E. Börger, E. Grädel and Y. Gurevich, The Classical Decision Problem. Springer (1997).
J. Bradfield and C. Stirling, Modal μ-calculi, in Handbook of Modal Logic, edited by P. Blackburn, J. van Benthem and F. Wolter. Elsevier (2007) 721–756.
Dawar, A., Grädel, E. and Kreutzer, S., Inflationary fixed points in modal logic. ACM Trans. Comput. Log. 5 (2004) 282–315. Google Scholar
Fiebig, T., Helmer, S., Kanne, C.-C., Moerkotte, G., Neumann, J., Schiele, R. and Westmann, T., Anatomy of a native XML base management system. VLDB J. 11 (2002) 292–314. Google Scholar
Georgetown Protein Information Resource, Protein sequence database (2001). Available on http://www.cs.washington.edu/research/xmldatasets/
G. Gottlob and C. Koch, Monadic queries over tree-structured data, in Proc. of 17th Ann. IEEE Symp. on Logic in Computer Science, LICS ’02 (Copenhagen, July 2002). IEEE CS Press (2002) 189–202.
E. Grädel, M. Otto and E. Rosen, Undecidability results on two-variable logics, in Proc. of 14th Ann. Symp. on Theoretical Aspects of Computer Science, STACS ’97 (Lübeck, Feb./March 1997), Lect. Notes Comput. Sci. vol. 1200, edited by R. Reischuk and M. Morvan, Springer (1997) 249–260.
N. Immerman, Descriptive Complexity. Springer (1999).
H.V. Jagadish, L.V.S. Lakshmanan, D. Srivastava and K. Thompson, TAX: A tree algebra for XML, in Revised Papers from 8th Int. Workshop on Database Programming Languages, DBPL 2001 (Frascati, Sept. 2001), Lect. Notes Comput. Sci. vol. 2397, edited by G. Ghelli and G. Grahne, Springer (2002) 149–164.
D. Janin and I. Walukiewicz, On the expressive completeness of the propositional mu-calculus with respect to monadic second order logic, in Proc. of 7th Int. Conf. on Concurrency Theory, CONCUR 1996 (Pisa, Aug. 1996), Lect. Notes Comput. Sci. vol. 1119, edited by U. Montanari and V. Sassone, Springer (1996) 263–277.
M. Marx, XPath with conditional axis relations, in Proc. of 9th Int. Conf. on Extending Database Technology, EDBT 2004 (Heraclion, March 2004), Lect. Notes Comput. Sci. vol. 2992, edited by E. Bertino et al., Springer (2004) 477–494.
Marx, M. and de Rijke, M., Semantic characterizations of navigational XPath. ACM SIGMOD Record 34 (2005) 41–46. Google Scholar
B. ten Cate, Regular XPath: algebra, logic and automata, unpublished note presented at AUTOMATHA Workshop on Algebraic Theory of Automata and Logic (2006).
Thomas, W., Languages, automata, and logic, Handbook of Formal Languages, Beyond Words vol. 3, edited by G. Rozenberg and A. Salomaa, Springer (1997) 389–455.
XML path language (XPath) version 1.0, edited by J. Clark and S. DeRose. World Wide Web Consortium (1999). http://www.w3.org/TR/xpath/.
XML path language (XPath) 2.0, edited by A. Berglund et al. World Wide Web Consortium (2007). Available on http://www.w3.org/TR/xpath20/.
XQuery 1.0 : An XML query language, edited by S. Boag et al. World Wide Web Consortium (2007). Available on http://www.w3.org/TR/xquery/.