## Decidable containment of recursive queries

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Venue: | Theoretical Computer Science |

Citations: | 25 - 4 self |

### BibTeX

@ARTICLE{Calvanese_decidablecontainment,

author = {Diego Calvanese and Moshe Y. Vardi},

title = {Decidable containment of recursive queries},

journal = {Theoretical Computer Science},

year = {},

pages = {2005}

}

### Years of Citing Articles

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### Abstract

Abstract. One of the most important reasoning tasks on queries is checking containment, i.e., verifying whether one query yields necessarily a subset of the result of another one. Query containment, is crucial in several contexts, such as query optimization, query reformulation, knowledge-base verification, information integration, integrity checking, and cooperative answering. Containment is undecidable in general for Datalog, the fundamental language for expressing recursive queries. On the other hand, it is known that containment between monadic Datalog queries and between Datalog queries and unions of conjunctive queries are decidable. It is also known that containment between unions of conjunctive two-way regular path queries (UC2RPQs), which are queries used in the context of semistructured data models containing a limited form of recursion in the form of transitive closure, is decidable. In this paper we combine the automata-theoretic techniques at the base of these two decidability results to show that containment of Datalog in UC2RPQs is decidable in 2EXPTIME. 1

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Citation Context ...lly, a CQ is a project-join query. By adding union and recursion to conjunctive queries, one gets Datalog, the language of logic programs (known also as Horn-clause programs) without function symbols =-=[15]-=-, which is essentially a fragment of fixpoint logic [16,17]. Datalog consists, in a pure way, only of the most fundamental elements of relational queries: join, projection, union, and recursion. With ... |

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Citation Context ... expressed using XML-like languages [27,28] and is accepted as a standard model for semistructured data [29,30]. In this framework, a basic querying mechanism is the one of regular path queries (RPQ) =-=[29,31,32]-=-, which ask for all pairs of objects that are connected by a path conforming to a regular expression. Regular path queries are extremely useful for expressing complex navigations in a graph. In partic... |

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Citation Context ...le query languages have been designed for retaining decidability. The same is true in databases, where the notion of conjunctive query is the basic one in the investigation of reasoning about queries =-=[14]-=-. A conjunctive query (CQ) is simply a conjunction of atoms, where each atom is built out from relation symbols and (existentially quantified) variables. Relationally, a CQ is a project-join query. By... |

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Citation Context ... in AI [1,2], is crucial in several contexts, such as query optimization, query reformulation, knowledge-base verification, information integration, integrity checking, and cooperative answering; cf. =-=[3,4,5,6,7,8,9,10,11,12,13]-=-. Thus, it is fair to describe query containment as one of the most fundamental database reasoning tasks. D. Calvanese et al. (Eds.): ICDT 2003, LNCS 2572, pp. 330–345, 2003. c○ Springer-Verlag Berlin... |

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Citation Context ...ct that the binary relation denoted by the label holds for the objects. This model captures data expressed using XML-like languages [27,28] and is accepted as a standard model for semistructured data =-=[29,30]-=-. In this framework, a basic querying mechanism is the one of regular path queries (RPQ) [29,31,32], which ask for all pairs of objects that are connected by a path conforming to a regular expression.... |

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Citation Context ...uld support. One of the most important is checking containment, i.e., verifying whether one query yields necessarily a subset of the result of another one. Query containment, called subsumption in AI =-=[1,2]-=-, is crucial in several contexts, such as query optimization, query reformulation, knowledge-base verification, information integration, integrity checking, and cooperative answering; cf. [3,4,5,6,7,8... |

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Citation Context ...ecursion to conjunctive queries, one gets Datalog, the language of logic programs (known also as Horn-clause programs) without function symbols [15], which is essentially a fragment of fixpoint logic =-=[16,17]-=-. Datalog consists, in a pure way, only of the most fundamental elements of relational queries: join, projection, union, and recursion. With respect to query containment, CQs and Datalog span the spec... |

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Citation Context ...) is a (labeled) tree and g isanodeof T ,weuseτ(g) to denote V (g). Two-way alternating tree automata (2ATAs) [35,23], are a generalization of standard nondeterministic top-down tree automata (1NTAs) =-=[38,39]-=-) with both upward moves and with alternation. Let B(I) be the set of positive Boolean formulae over I, built inductively by applying ∧ and ∨ starting from true, false, and elements of I. ForasetJ ⊆ I... |

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Citation Context |

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Citation Context ... expressed using XML-like languages [27,28] and is accepted as a standard model for semistructured data [29,30]. In this framework, a basic querying mechanism is the one of regular path queries (RPQ) =-=[29,31,32]-=-, which ask for all pairs of objects that are connected by a path conforming to a regular expression. Regular path queries are extremely useful for expressing complex navigations in a graph. In partic... |

140 |
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Citation Context ...ry containment, CQs and Datalog span the spectrum in terms of computational complexity. In [14] it is shown that CQ containment is equivalent to CQ evaluation (NP-complete). (For some extensions, see =-=[18,19,20,21]-=-.) On the other hand, it is shown in [22] that containment of Datalog queries is undecidable; the proof is by reduction from the containment problem for context-free grammars. The most powerful query-... |

136 |
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Citation Context ...ry containment, CQs and Datalog span the spectrum in terms of computational complexity. In [14] it is shown that CQ containment is equivalent to CQ evaluation (NP-complete). (For some extensions, see =-=[18,19,20,21]-=-.) On the other hand, it is shown in [22] that containment of Datalog queries is undecidable; the proof is by reduction from the containment problem for context-free grammars. The most powerful query-... |

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Citation Context ...t containment of Datalog queries is undecidable; the proof is by reduction from the containment problem for context-free grammars. The most powerful query-containment results for Datalog are given in =-=[23,24, 25]-=-. In [23] it is pointed out that tree-automata techniques can be used to prove the decidability of query containment for monadic Datalog, where rule heads use a single variable (which means that inter... |

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Citation Context ...t containment of Datalog queries is undecidable; the proof is by reduction from the containment problem for context-free grammars. The most powerful query-containment results for Datalog are given in =-=[23,24, 25]-=-. In [23] it is pointed out that tree-automata techniques can be used to prove the decidability of query containment for monadic Datalog, where rule heads use a single variable (which means that inter... |

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Citation Context ... one can construct conjunctive 2-way regular path queries (C2RPQs), which enables us to perform joins and projections over 2RPQs. C2RPQs are the basic building blocks for querying semistructured data =-=[33,13,31]-=-. The containment problem for C2RPQs (actually for UC2RPQs, unions of such C2RPQs) was studied in [34] (see also [33]), where it was shown, using two-way automata, to be EXPSPACE-complete. The notable... |

79 |
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Citation Context ...t containment of Datalog queries is undecidable; the proof is by reduction from the containment problem for context-free grammars. The most powerful query-containment results for Datalog are given in =-=[23,24, 25]-=-. In [23] it is pointed out that tree-automata techniques can be used to prove the decidability of query containment for monadic Datalog, where rule heads use a single variable (which means that inter... |

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Citation Context ...ry containment, CQs and Datalog span the spectrum in terms of computational complexity. In [14] it is shown that CQ containment is equivalent to CQ evaluation (NP-complete). (For some extensions, see =-=[18,19,20,21]-=-.) On the other hand, it is shown in [22] that containment of Datalog queries is undecidable; the proof is by reduction from the containment problem for context-free grammars. The most powerful query-... |

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Citation Context ...in terms of computational complexity. In [14] it is shown that CQ containment is equivalent to CQ evaluation (NP-complete). (For some extensions, see [18,19,20,21].) On the other hand, it is shown in =-=[22]-=- that containment of Datalog queries is undecidable; the proof is by reduction from the containment problem for context-free grammars. The most powerful query-containment results for Datalog are given... |

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Citation Context ...uld support. One of the most important is checking containment, i.e., verifying whether one query yields necessarily a subset of the result of another one. Query containment, called subsumption in AI =-=[1,2]-=-, is crucial in several contexts, such as query optimization, query reformulation, knowledge-base verification, information integration, integrity checking, and cooperative answering; cf. [3,4,5,6,7,8... |

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Citation Context ...ojections over 2RPQs. C2RPQs are the basic building blocks for querying semistructured data [33,13,31]. The containment problem for C2RPQs (actually for UC2RPQs, unions of such C2RPQs) was studied in =-=[34]-=- (see also [33]), where it was shown, using two-way automata, to be EXPSPACE-complete. The notable fact about the decidability of containment for C2RPQs is that C2RPQs are a fragment of recursive Data... |

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Citation Context ...sent objects, and a labeled edge between two nodes represents the fact that the binary relation denoted by the label holds for the objects. This model captures data expressed using XML-like languages =-=[27,28]-=- and is accepted as a standard model for semistructured data [29,30]. In this framework, a basic querying mechanism is the one of regular path queries (RPQ) [29,31,32], which ask for all pairs of obje... |

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Citation Context ...nadic Datalog. The class UC2RPQ has several features that are typical of modern query languages for knowledge and data bases. In particular, it is the largest fragment of query languages for XML data =-=[41]-=- for which containment is known to be decidable [34]. The 2EXPTIME upper-bound result shows that adding transitive closure to conjunctive queries does not increase the complexity of query containment ... |

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Citation Context ...lphabet Σ, there is a 2ATA A∪ of size polynomial in the sum of the sizes of A1,...,An such that T (A∪) =T (A1) ∪···∪T(An). We make also use of the following standard results for 1NTAs. Proposition 3 (=-=[40]-=-). Given 1NTAs A1 and A2 over an alphabet Σ, there is a 1NTA A∩ of size polynomial in the size of A1 and A2 such that T (A∩) = T (A1) ∩T(A2). Proposition 4 ([38,39]). The nonemptiness problem for 1NTA... |