Abstract | ||
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We study the definability problem for first-order logic, denoted by FO-Def. The input of FO-Def is a relational database instance I and a relation R; the question to answer is whether there exists a first-order query Q (or, equivalently, a relational algebra expression Q) such that Q evaluated on I gives R as an answer.
Although the study of FO-Def dates back to 1978, when the decidability of this problem was shown, the exact complexity of FO-Def remains as a fundamental open problem. In this article, we provide a polynomial-time algorithm for solving FO-Def that uses calls to a graph-isomorphism subroutine (or oracle). As a consequence, the first-order definability problem is found to be complete for the class GI of all problems that are polynomial-time Turing reducible to the graph isomorphism problem, thus closing the open question about the exact complexity of this problem. The technique used is also applied to a generalized version of the problem that accepts a finite set of relation pairs, and whose exact complexity was also open; this version is also found to be GI-complete.
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Year | DOI | Venue |
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2016 | 10.1145/2886095 | ACM Trans. Database Syst. |
Keywords | Field | DocType |
Definability problem, expressiveness, first-order logic, relational algebra | Finite set,Open problem,Existential quantification,Relational database,Computer science,Decidability,First-order logic,Relational algebra,Graph isomorphism problem,Database | Journal |
Volume | Issue | ISSN |
41 | 2 | 0362-5915 |
Citations | PageRank | References |
1 | 0.35 | 0 |
Authors | ||
2 |
Name | Order | Citations | PageRank |
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Marcelo Arenas | 1 | 2618 | 193.91 |
Gonzalo I. Diaz | 2 | 29 | 2.72 |