Relative expressive power of navigational querying on graphs

Abstract

Document VersionPublisher's PDF, also known as Version of Record (includes final page, issue and volume numbers)Please check the document version of this publication:• A submitted manuscript is the author's version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and page numbers. General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. Link to publication• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.• You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal ? Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Motivated by both established and new applications, we study navigational query languages for graphs (binary relations). The simplest language has only the two operators union and composition, together with the identity relation. We make more powerful languages by adding any of the following operators: intersection; set difference; projection; coprojection; converse; and the diversity relation. All these operators map binary relations to binary relations. We compare the expressive power of all resulting languages. We do this not only for general path queries (queries where the result may be any binary relation) but also for boolean or yes/no queries (expressed by the nonemptiness of an expression). For both cases, we present the complete Hasse diagram of relative expressiveness. In particular the Hasse diagram for boolean queries contains some nontrivial separations and a few surprising collapses.

Relative expressive power of downward fragments of navigational query languages on trees and chains

“…In several cases, we were able to argue that pairs of downward fragments of the navigational query languages that are not equivalent in expressive power when used to query graphs, are already not equivalent in expressive power on the simplest of graphs: labeled or unlabeled chains. Hence, for these languages, we actually strengthen the results of Fletcher et al [8].…”

“…Observe that [8]. We also observe that we can carry over subsumption results from one type of graph to another, considering the relationships of Figure 2.…”

“…Homomorphisms are often used to prove properties of query languages, including expressiveness results [8]. We use homomorphisms to show several results, including a major collapse result for boolean queries on unlabeled trees and unlabeled chains: we show that only fragments with the non-monotone 1 operator π can express queries that are not equivalent to queries of the form the height of the tree is at least k.…”

“…The subsumption results for the navigational query languages on graphs (both labeled an unlabeled) have already been studied in full detail [8][9][10][11]. We summarize the results that are relevant to us in this paper.…”

“…The core navigational power of these query languages can be captured by various fragments of the calculus of relations, popularized by Tarski, extended with transitive closure [13,22]. In the form of the navigational query languages of Fletcher et al [8], the relative expressive power of these fragments have been studied in full detail on graph-structured data [9][10][11]. Much less is known for the more restrictive tree data model, however: most of the results on graphs do not directly apply to trees.…”