XPath satisfiability with downward and sibling axes is tractable under most of real-world DTDs

• Authors: Yasunori Ishihara;Kenji Hashimoto;Shogo Shimizu;Toru Fujiwara
• Venue: Proceedings of the twelfth international workshop on Web information and data management
• Year: 2012

This paper aims at finding a subclass of DTDs that covers real-world DTDs but still has non-trivial tractability for XPath satisfiability problem. Known subclasses of DTDs, such as duplicate-free DTDs proposed by Montazerian et al. and disjunction-capsuled DTDs and their extension called DC?+-DTDs proposed by Ishihara et al., have tractability against various XPath classes but are somewhat smaller than real-world DTDs. In our examination, 6 out of 27 real-world DTDs are neither duplicate-free nor disjunction-capsuled. This paper proposes a subclass of DTDs, called RW-DTDs, as a model of real-world DTDs. RW-DTDs cover 26 out of the 27 real-world DTDs and 1406 out of the 1407 DTD rules. The idea for assuring the non-trivial tractability under RW-DTDs is twofold. One is to hybridize duplicate-free DTDs and disjunction-capsuled DTDs. In an RW-DTD, each part of the content model of each DTD rule must be either duplicate-free or disjunction-capsuled. Thus, RW-DTDs are a proper superclass of, but expected to inherit the tractability from, the two original classes. The other is to introduce into regular expressions a new operator representing "either or both." The new operator is useful for avoiding tag name duplication and non-capsuled disjunction in content models of DTD rules. Next, this paper shows that under RW-DTDs, XPath satisfiability with child, descendant-or-self, and sibling axes is tractable. Note that under arbitrary DTDs, satisfiability for the same XPath class is known to be NP-complete. Moreover, as non-trivial limitations, this paper also shows that RW-DTDs do not inherit the tractability from the two original classes when the XPath class contains parent axes or qualifiers.