On Core XPath with Inflationary Fixed Points

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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 prove that the satisfiability problem of this language is undecidable. In fact, the fragment of CXP+IFP containing only theselfanddescendantaxes is already undecidable.