Containment of Simple Regular Path Queries

Testing containment of queries is a fundamental reasoning task in knowledge representation. We study here the containment problem for Conjunctive Regular Path Queries (CRPQs), a navigational query language extensively used in ontology and graph database querying. While it is known that containment of CRPQs is expspace-complete in general, we focus here on severely restricted fragments, which are known to be highly relevant in practice according to several recent studies. We obtain a detailed overview of the complexity of the containment problem, depending on the features used in the regular expressions of the queries, with completeness results for np, pitwo, pspace or expspace

Optimization Properties for Classes of Conjunctive Regular Path Queries

We are interested in the theoretical foundations of the optimization of conjunctive regular path queries (CRPQs). The basic problem here is deciding query containment both in the absence and presence of constraints. Containment without constraints for CRPQs is EXPSPACE-complete, as opposed to only NP-complete for relational conjunctive queries. Our past experience with implementing similar algorithms suggests that staying in PSPACE might still be useful. Therefore we investigate the complexity of containment for a hierarchy of fragments of the CRPQ language. The classifying principle of the fragments is the expressivity of the regular path expressions allowed in the query atoms. For most of these fragments, we give matching lower and upper bounds for containment in the absence of constraints. We also introduce for every fragment a naturally corresponding class of constraints in whose presence we show both decidability and undecidability results for containment in various fragments. Finally, we apply our results to give a complete algorithm for rewriting with views in the presence of constraints for a fragment that contains Kleene-star and disjunction

Expressiveness and static analysis of extended conjunctive regular path queries

We study the expressiveness and the complexity of static analysis of extended conjunctive regular path queries (ECRPQs), introduced by Barceló et al. (2010) [3]. ECRPQs are an extension of conjunctive regular path querie s (CRPQs), a well-studied language for querying graph structured databases. Our first main result shows that query containment and equivalence of a CRPQ in an ECRPQ are undecidable. This settles one of the main open problems posed by Barceló et al. As a second main result, we prove a non-recursive succinctness gap between CRPQs and the CRPQ-expressible fragment of ECRPQs. Apart from this, we develop a tool for proving inexpressibility results for CRPQs and ECRPQs. In particular, this enables us to show that there exist queries definable by regular expressions with backreferencing, but not expressible by ECRPQs. © 2013 Elsevier Inc

Expressiveness and static analysis of extended conjunctive regular path queries

We study the expressiveness and the complexity of static analysis of extended conjunctive regular path queries (ECRPQs), introduced by Barceló et al. (PODS '10). ECRPQs are an extension of con- junctive regular path queries (CRPQs), a well-studied language for querying graph structured databases. Our first main result shows that query containment and equivalence of a CRPQ in an ECRPQ is undecidable. This settles one of the main open problems posed by Barceló et al. As a second main result, we prove a non-recursive succinctness gap between CRPQs and the CRPQ-expressible fragment of ECRPQs. Apart from this, we develop a tool for proving inexpressibility results for CRPQs and ECRPQs. In particular, this enables us to show that there exist queries definable by regular expressions with backreferencing, but not expressible by ECRPQs

Query Containment for Highly Expressive Datalog Fragments

The containment problem of Datalog queries is well known to be undecidable. There are, however, several Datalog fragments for which containment is known to be decidable, most notably monadic Datalog and several "regular" query languages on graphs. Monadically Defined Queries (MQs) have been introduced recently as a joint generalization of these query languages. In this paper, we study a wide range of Datalog fragments with decidable query containment and determine exact complexity results for this problem. We generalize MQs to (Frontier-)Guarded Queries (GQs), and show that the containment problem is 3ExpTime-complete in either case, even if we allow arbitrary Datalog in the sub-query. If we focus on graph query languages, i.e., fragments of linear Datalog, then this complexity is reduced to 2ExpSpace. We also consider nested queries, which gain further expressivity by using predicates that are defined by inner queries. We show that nesting leads to an exponentially increasing hierarchy for the complexity of query containment, both in the linear and in the general case. Our results settle open problems for (nested) MQs, and they paint a comprehensive picture of the state of the art in Datalog query containment.Comment: 20 page

Simulation Subsumption or Déjà vu on the Web

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

Exposing not only human-centered information, but machine-processable data on the Web is one of the commonalities of recent Web trends. It has enabled a new kind of applications and businesses where the data is used in ways not foreseen by the data providers. Yet this exposition has fractured the Web into islands of data, each in different Web formats: Some providers choose XML, others RDF, again others JSON or OWL, for their data, even in similar domains. This fracturing stifles innovation as application builders have to cope not only with one Web stack (e.g., XML technology) but with several ones, each of considerable complexity. With Xcerpt we have developed a rule- and pattern based query language that aims to give shield application builders from much of this complexity: In a single query language XML and RDF data can be accessed, processed, combined, and re-published. Though the need for combined access to XML and RDF data has been recognized in previous work (including the W3C’s GRDDL), our approach differs in four main aspects: (1) We provide a single language (rather than two separate or embedded languages), thus minimizing the conceptual overhead of dealing with disparate data formats. (2) Both the declarative (logic-based) and the operational semantics are unified in that they apply for querying XML and RDF in the same way. (3) We show that the resulting query language can be implemented reusing traditional database technology, if desirable. Nevertheless, we also give a unified evaluation approach based on interval labelings of graphs that is at least as fast as existing approaches for tree-shaped XML data, yet provides linear time and space querying also for many RDF graphs. We believe that Web query languages are the right tool for declarative data access in Web applications and that Xcerpt is a significant step towards a more convenient, yet highly efficient data access in a “Web of Data”