### Abstract

We consider the problem of answering queries using views, where queries and views are conjunctive queries with arithmetic comparisons over dense orders. Previous work only considered limited variants of this problem, without giving a complete solution. We first show that obtaining equivalent rewritings for conjunctive queries with arithmetic comparisons is decidable. Then, we consider the problem of finding maximally contained rewritings (MCRs) where the decidability proof does not carry over. We investigate two special cases of this problem where the query uses only semi-interval comparisons. In both cases decidability of finding MCRs depends on the query containment test. First, we address the case where the homomorphism property holds in testing query containment. In this case decidability is easy to prove but developing an efficient algorithm is not trivial. We develop such an algorithm and prove that it is sound and complete. This algorithm applies in many cases where the query uses only left (or right) semi-interval comparisons. Then, we develop a new query containment test for the case where the containing query uses both left and right semi-interval comparisons but with only one left (or right) semi-interval subgoal. Based on this test, we show how to produce an MCR which is a Datalog query with arithmetic comparisons. The containment test that we develop obtains a result of independent interest. It finds another special case where query containment in the presence of arithmetic comparisons can be tested in nondeterministic polynomial time.

Original language | English |
---|---|

Pages (from-to) | 88-123 |

Number of pages | 36 |

Journal | Theoretical Computer Science |

Volume | 368 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - 5 Dec 2006 |

Externally published | Yes |

### Fingerprint

### Keywords

- Databases
- Query languages
- Query rewriting

### ASJC Scopus subject areas

- Computational Theory and Mathematics

### Cite this

*Theoretical Computer Science*,

*368*(1-2), 88-123. https://doi.org/10.1016/j.tcs.2006.08.020

**Rewriting queries using views in the presence of arithmetic comparisons.** / Afrati, Foto; Li, Chen; Mitra, Prasenjit.

Research output: Contribution to journal › Article

*Theoretical Computer Science*, vol. 368, no. 1-2, pp. 88-123. https://doi.org/10.1016/j.tcs.2006.08.020

}

TY - JOUR

T1 - Rewriting queries using views in the presence of arithmetic comparisons

AU - Afrati, Foto

AU - Li, Chen

AU - Mitra, Prasenjit

PY - 2006/12/5

Y1 - 2006/12/5

N2 - We consider the problem of answering queries using views, where queries and views are conjunctive queries with arithmetic comparisons over dense orders. Previous work only considered limited variants of this problem, without giving a complete solution. We first show that obtaining equivalent rewritings for conjunctive queries with arithmetic comparisons is decidable. Then, we consider the problem of finding maximally contained rewritings (MCRs) where the decidability proof does not carry over. We investigate two special cases of this problem where the query uses only semi-interval comparisons. In both cases decidability of finding MCRs depends on the query containment test. First, we address the case where the homomorphism property holds in testing query containment. In this case decidability is easy to prove but developing an efficient algorithm is not trivial. We develop such an algorithm and prove that it is sound and complete. This algorithm applies in many cases where the query uses only left (or right) semi-interval comparisons. Then, we develop a new query containment test for the case where the containing query uses both left and right semi-interval comparisons but with only one left (or right) semi-interval subgoal. Based on this test, we show how to produce an MCR which is a Datalog query with arithmetic comparisons. The containment test that we develop obtains a result of independent interest. It finds another special case where query containment in the presence of arithmetic comparisons can be tested in nondeterministic polynomial time.

AB - We consider the problem of answering queries using views, where queries and views are conjunctive queries with arithmetic comparisons over dense orders. Previous work only considered limited variants of this problem, without giving a complete solution. We first show that obtaining equivalent rewritings for conjunctive queries with arithmetic comparisons is decidable. Then, we consider the problem of finding maximally contained rewritings (MCRs) where the decidability proof does not carry over. We investigate two special cases of this problem where the query uses only semi-interval comparisons. In both cases decidability of finding MCRs depends on the query containment test. First, we address the case where the homomorphism property holds in testing query containment. In this case decidability is easy to prove but developing an efficient algorithm is not trivial. We develop such an algorithm and prove that it is sound and complete. This algorithm applies in many cases where the query uses only left (or right) semi-interval comparisons. Then, we develop a new query containment test for the case where the containing query uses both left and right semi-interval comparisons but with only one left (or right) semi-interval subgoal. Based on this test, we show how to produce an MCR which is a Datalog query with arithmetic comparisons. The containment test that we develop obtains a result of independent interest. It finds another special case where query containment in the presence of arithmetic comparisons can be tested in nondeterministic polynomial time.

KW - Databases

KW - Query languages

KW - Query rewriting

UR - http://www.scopus.com/inward/record.url?scp=33750731959&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33750731959&partnerID=8YFLogxK

U2 - 10.1016/j.tcs.2006.08.020

DO - 10.1016/j.tcs.2006.08.020

M3 - Article

AN - SCOPUS:33750731959

VL - 368

SP - 88

EP - 123

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

IS - 1-2

ER -