Satisfiability of XPath Queries with Sibling Axes

Abstract

Abstract. We study the satisfiability problem for XPath fragments supporting the following-sibling and preceding-sibling axes. Although this problem was recently studied for XPath fragments without sibling axes, little is known about the impact of the sibling axes on the satisfiability analysis. To this end we revisit the satisfiability problem for a variety of XPath fragments with sibling axes, in the presence of DTDs, in the absence of DTDs, and under various restricted DTDs. In these settings we establish complexity bounds ranging from NLOGSPACE to undecidable. Our main conclusion is that in many cases, the presence of sibling axes complicates the satisfiability analysis. Indeed, we show that there are XPath satisfiability problems that are in PTIME and PSPACE in the absence of sibling axes, but that become NP-hard and EXPTIME-hard, respectively, when sibling axes are used instead of the corresponding vertical modalities (e.g., the wildcard and the descendant axis).

Alternation-free modal mu-calculus for data trees

“…The fragment of XPath [7] below contains all operators commonly found in practice and was considered in [2,17]. The grammars of queries p and qualifiers q are mutually recursive.…”

“…The semantics of queries and qualifiers is standard (cf., e.g., [17]). We write the satisfaction relations as τ, n, n |= p and τ, n |= q, where τ is an XML tree over Σ and Σ with root n R , and n and n are Σ-labelled nodes.…”

“…The most basic static analysis problem for XPath, with a variety of applications, is satisfiability in the presence of DTDs. The two recent surveys on its complexity by Benedikt, Fan and Geerts [2,17] convey that relatively little is known for fragments with negation and data (i.e., equality comparisons between attribute values). The only decidability result in [2,17] that allows negation and data does not allow axes which are recursive (such as "self or descendant") or between siblings.…”

“…The two recent surveys on its complexity by Benedikt, Fan and Geerts [2,17] convey that relatively little is known for fragments with negation and data (i.e., equality comparisons between attribute values). The only decidability result in [2,17] that allows negation and data does not allow axes which are recursive (such as "self or descendant") or between siblings. By representing XML documents as data trees and translating from XPath to FO 2 (+1, ∼), a decidable fragment with negation, data and all nonrecursive axes was obtained in [4].…”

Bounded Depth Data Trees

“…The data values are used to model the content of the document. Recently, there has been flurry of research on models with data, including data words [19,31,13,14,5,22,3], and data trees [8,1,4,16,6].…”