Simulation Subsumption or Déjà vu on the Web

Abstract

Abstract. Simulation unification is a special kind of unification adapted to retrieving semi-structured data on the Web. This article introduces simulation subsumption, or containment, that is, query subsumption under simulation unification. Simulation subsumption is crucial in general for query optimization, in particular for optimizing pattern-based search engines, and for the termination of recursive rule-based web languages such as the XML and RDF query language Xcerpt. This paper first motivates and formalizes simulation subsumption. Then, it establishes decidability of simulation subsumption for advanced query patterns featuring descendant constructs, regular expressions, negative subterms (or subterm exclusions), and multiple variable occurrences. Finally, we show that subsumption between two query terms can be decided in O(n! n ) where n is the sum of the sizes of both query terms.

Four Lessons in Versatility or How Query Languages Adapt to the Web

“…35 This result shows that while Xcerpt is indeed Turing complete that expressive power is justified as it can express all computable queries modulo deep equal. Since the whole language is Turing complete, it is worth investigating sub-languages with better computational properties.…”

“…Then there is an injective mapping π from ChildT + (q 1 ) to ChildT + (q 2 ) such that q i 1 subsumes π(q i 1 ) for all q i 1 ∈ ChildT + (q 1 ). Furthermore, if q 1 and q 2 are breadth-incomplete, then there is a (not necessarily injective) mapping σ from ChildT − (q 1 ) to ChildT − (q 2 ) such that pos(σ(q Lemma 1 immediately follows from the equivalence of the subsumption relationship and the extended query term simulation (see Lemma 4 in the appendix of [35]). …”

“…This process can be repeated until q 1 has been transformed into a simulation equivalent version of q 2 . For the proof, see the appendix of [35].…”

“…For the sake of brevity this full definition of extended ground query term simulation is given in the appendix of [35].…”

“…-if the label of q is a regular expression e, this regular expression may be replaced by any label that matches with e, or any other regular expression e which is subsumed by e (see Definition 8 in the appendix of [35]). 41 e ∈ RE, e subsumes e' ⇒ e{{q 1 , .…”