XPath Satisfiability with Parent Axes or Qualifiers Is Tractable under Many of Real-World DTDs
Yasunori Ishihara, Nobutaka Suzuki, Kenji Hashimoto, Shogo Shimizu,, Toru Fujiwara

TL;DR
This paper introduces MRW-DTDs, a new subclass of DTDs that enables polynomial-time XPath satisfiability checking with parent axes or qualifiers, covering most real-world DTDs and expanding tractability.
Contribution
The paper proposes MRW-DTDs, a subclass of DTDs that extends tractability of XPath satisfiability to include parent axes and qualifiers, improving upon previous RW-DTDs.
Findings
MRW-DTDs cover 24 of 27 real-world DTDs.
XPath satisfiability with parent axes is tractable under MRW-DTDs.
XPath satisfiability with qualifiers is tractable under MRW-DTDs.
Abstract
This paper aims at finding a subclass of DTDs that covers many of the real-world DTDs while offering a polynomial-time complexity for deciding the XPath satisfiability problem. In our previous work, we proposed RW-DTDs, which cover most of the real-world DTDs (26 out of 27 real-world DTDs and 1406 out of 1407 DTD rules). However, under RW-DTDs, XPath satisfiability with only child, descendant-or-self, and sibling axes is tractable. In this paper, we propose MRW-DTDs, which are slightly smaller than RW-DTDs but have tractability on XPath satisfiability with parent axes or qualifiers. MRW-DTDs are a proper superclass of duplicate-free DTDs proposed by Montazerian et al., and cover 24 out of the 27 real-world DTDs and 1403 out of the 1407 DTD rules. Under MRW-DTDs, we show that XPath satisfiability problems with (1) child, parent, and sibling axes, and (2) child and sibling axes and…
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Taxonomy
TopicsCryptography and Data Security · semigroups and automata theory · Logic, programming, and type systems
