An Automata-Theoretic Approach to Regular XPath

Abstract

In this paper we present Regular XPath (RXPath), which is a natural extension of XPath with regular expressions over paths that has the same computational properties as XPath: linear-time query evaluation and exponential-time reasoning. To establish these results, we devise a unifying automata-theoretic framework based on two-way weak alternating tree automata. Specifically, we consider automata that have infinite runs on finite trees. This enables us to leverage and simplify existing automata-theoretic machinery and develop algorithms both for query evaluation and for reasoning over queries. With respect to the latter problem, we consider RXPath as a constraint language, and study constraint satisfiability, and query satisfiability and containment under constraints in the setting of RXPath.

Static analysis of XML security views and query rewriting

“…Building an automaton from an X Reg expression is in Exptime (see [6]). Hence, the Exptime upper bound follows from Proposition 10.…”

“…Hence, the Exptime upper bound follows from Proposition 10. To show Exptime-hardness, we reduce satisfiability of X Reg (see [9,23]) to testing interval boundedness. Let Q be a X Reg expression over an alphabet Σ.…”

“…A has state space S -roughly corresponding to the subformula of X -of linear size, of course. This alternating automaton A is translated in exponential time into a standard tree automaton A I such that for every tree t, A I accepts t if and only if X is satisfied in t. Actually, the construction in [6] works over first-child-next-sibling encoding, but the translation to VPA is obvious, using [16] for instance, so that we can assume A I to be a VPA pΣ, Q, Γ, I, F, Rq.…”

“…Furthermore, although this result is not mentionned in [6], a careful analysis of the rules for constructing R guarantees that we can check the transitions of A I using only polynomial time: in the VPA setting, this means that for every q, q I P Q, γ P Γ, η P top, clu and a P Σ, we can check that q pη,aq:γ ÝÝÝÝÑ q I belongs to R using polynomial time.…”

“…To begin, we first check that Q 1 ¤ 1 Q 2 , in polynomial space by Theorem 10. Using the method in [6] we can build in exponential time two automata A 1 and A 2 over Σ ¢ t0, 1u such that A 1 (resp. A 2 ) recognizes the language A Q1 (resp.…”