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.
@article{ITA_2013__47_1_3_0, author = {Afanasiev, Loredana and Cate, Balder Ten}, title = {On Core XPath with Inflationary Fixed Points}, journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications}, volume = {47}, year = {2013}, pages = {3-23}, doi = {10.1051/ita/2012027}, mrnumber = {3072309}, zbl = {1270.68100}, language = {en}, url = {http://dml.mathdoc.fr/item/ITA_2013__47_1_3_0} }
Afanasiev, Loredana; Cate, Balder Ten. On Core XPath with Inflationary Fixed Points. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 47 (2013) pp. 3-23. doi : 10.1051/ita/2012027. http://gdmltest.u-ga.fr/item/ITA_2013__47_1_3_0/
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