# On Core XPath with Inflationary Fixed Points

Loredana Afanasiev; Balder Ten Cate

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2013)

- Volume: 47, Issue: 1, page 3-23
- ISSN: 0988-3754

## Access Full Article

top## Abstract

top## How to cite

topAfanasiev, Loredana, and Cate, Balder Ten. "On Core XPath with Inflationary Fixed Points." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 47.1 (2013): 3-23. <http://eudml.org/doc/272985>.

@article{Afanasiev2013,

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

author = {Afanasiev, Loredana, Cate, Balder Ten},

journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},

keywords = {modal logic; fixed points; XML databases; XPath; Xpath},

language = {eng},

number = {1},

pages = {3-23},

publisher = {EDP-Sciences},

title = {On Core XPath with Inflationary Fixed Points},

url = {http://eudml.org/doc/272985},

volume = {47},

year = {2013},

}

TY - JOUR

AU - Afanasiev, Loredana

AU - Cate, Balder Ten

TI - On Core XPath with Inflationary Fixed Points

JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

PY - 2013

PB - EDP-Sciences

VL - 47

IS - 1

SP - 3

EP - 23

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

LA - eng

KW - modal logic; fixed points; XML databases; XPath; Xpath

UR - http://eudml.org/doc/272985

ER -

## References

top- [1] 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.
- [2] 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.
- [3] P. Blackburn, M. de Rijke and Y. Venema, Modal Logic, Cambridge Tracts in Theoretical Computer Science, Cambridge University Press 53 (2002). Zbl0988.03006
- [4] 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.
- [5] E. Börger, E. Grädel and Y. Gurevich, The Classical Decision Problem. Springer (1997). Zbl0970.03001MR1482227
- [6] 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.
- [7] A. Dawar, E. Grädel and S. Kreutzer, Inflationary fixed points in modal logic. ACM Trans. Comput. Log.5 (2004) 282–315. Zbl0999.03019MR2053398
- [8] T. Fiebig, S. Helmer, C.-C. Kanne, G. Moerkotte, J. Neumann, R. Schiele and T. Westmann, Anatomy of a native XML base management system. VLDB J.11 (2002) 292–314. Zbl1047.68046
- [9] Georgetown Protein Information Resource, Protein sequence database (2001). Available on http://www.cs.washington.edu/research/xmldatasets/
- [10] 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.
- [11] 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. Zbl0927.03015MR1473779
- [12] N. Immerman, Descriptive Complexity. Springer (1999). Zbl0918.68031MR1732784
- [13] 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. Zbl1098.68553
- [14] 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.
- [15] 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.
- [16] M. Marx and M. de Rijke, Semantic characterizations of navigational XPath. ACM SIGMOD Record34 (2005) 41–46.
- [17] B. ten Cate, Regular XPath: algebra, logic and automata, unpublished note presented at AUTOMATHA Workshop on Algebraic Theory of Automata and Logic (2006).
- [18] W. Thomas, Languages, automata, and logic, Handbook of Formal Languages, Beyond Words vol. 3, edited by G. Rozenberg and A. Salomaa, Springer (1997) 389–455.
- [19] 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/.
- [20] 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/.
- [21] 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/.

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.