Equivalences among aggregate queries with negation

Cohen, Sara; Sagiv, Yehoshua; Nutt, Werner

doi:10.1145/1055686.1055691

Cited by 24 publications

(3 citation statements)

References 17 publications

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“…Prior work in the database community mainly focused on the theoretical study of decidability [13,29] or generating a comprehensive set of test databases to "kill" as many erroneous queries as possible [11], but does not pay much attention to explaining why two queries are inequivalent. There are recent systems that aim to generate counterexamples for SQL queries.…”

Section: Introductionmentioning

confidence: 99%

Explaining Wrong Queries Using Small Examples

Miao

Roy

Yang

2019

Proceedings of the 2019 International Conference on Management of Data

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For testing the correctness of SQL queries, e.g., evaluating student submissions in a database course, a standard practice is to execute the query in question on some test database instance and compare its result with that of the correct query. Given two queries Q1 and Q2, we say that a database instance D is a counterexample (for Q1 and Q2) if Q1(D) differs from Q2(D); such a counterexample can serve as an explanation of why Q1 and Q2 are not equivalent. While the test database instance may serve as a counterexample, it may be too large or complex to read and understand where the inequivalence comes from. Therefore, in this paper, given a known counterexample D for Q1 and Q2, we aim to find the smallest counterexample D′ ⊆ D where Q1(D′) ≠ Q2(D′). The problem in general is NP-hard. We give a suite of algorithms for finding the smallest counterexample for different classes of queries, some more tractable than others. We also present an efficient provenance-based algorithm for SPJUD queries that uses a constraint solver, and extend it to more complex queries with aggregation, group-by, and nested queries. We perform extensive experiments indicating the effectiveness and scalability of our solution on student queries from an undergraduate database course and on queries from the TPC-H benchmark. We also report a user study from the course where we deployed our tool to help students with an assignment on relational algebra.

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Section: Introductionmentioning

confidence: 99%

Explaining Wrong Queries Using Small Examples

Miao

Roy

Yang

2019

Proceedings of the 2019 International Conference on Management of Data

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“…See the SystemML Engine Developer Guide for details on the weighted-square loss operator wsloss 2. This was claimed, for conjunctive queries only, in Theorem 5.2 in[3] but a proof was never produced; a proof was given for bag-set semantics in[4]. See the discussion in[8].…”

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confidence: 99%

SPORES: Sum-Product Optimization via Relational Equality Saturation for Large Scale Linear Algebra

Wang¹,

Hutchison²,

Leang³

et al. 2020

Preprint

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Machine learning algorithms are commonly specified in linear algebra (LA). LA expressions can be rewritten into more efficient forms, by taking advantage of input properties such as sparsity, as well as program properties such as common subexpressions and fusible operators. The complex interaction among these properties' impact on the execution cost poses a challenge to optimizing compilers. Existing compilers resort to intricate heuristics that complicate the codebase and add maintenance cost but fail to search through the large space of equivalent LA expressions to find the cheapest one. We introduce a general optimization technique for LA expressions, by converting the LA expressions into Relational Algebra (RA) expressions, optimizing the latter, then converting the result back to (optimized) LA expressions. One major advantage of this method is that it is complete, meaning that any equivalent LA expression can be found using the equivalence rules in RA. The challenge is the major size of the search space, and we address this by adopting and extending a technique used in compilers, called equality saturation. We integrate the optimizer into SystemML and validate it empirically across a spectrum of machine learning tasks; we show that we can derive all existing hand-coded optimizations in SystemML, and perform new optimizations that lead to speedups from 1.2X to 5X.Optimization opportunities like this are ubiquitous in machine learning programs. State-of-the-art optimizing compilers such as SystemML [1], OptiML [27], and Cumulon[11] commonly implement syntactic rewrite rules that exploit the algebraic properties of the LA expressions. For example, SystemML includes a rule that rewrites the preceding

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“…The problem of deciding equivalence among conjunctive aggregate count-distinct queries has been investigated starting from late 90s, and the problem is known to be decidable for most of the aggregate operators [3,5,1,2,5] including SUM, Average, and COUNT. For for count-distinct queries, although some sufficient conditions have been proposed [5,2], it has still been open if the problem is decidable or not.…”

Section: Introductionmentioning

confidence: 99%

Decidability of Equivalence of Aggregate Count-Distinct Queries

Hariri,

Tannen

2015

Preprint

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We address the problem of equivalence of count-distinct aggregate queries, prove that the problem is decidable, and can be decided in the third level of Polynomial hierarchy. We introduce the notion of core for conjunctive queries with comparisons as an extension of the classical notion for relational queries, and prove that the existence of isomorphism among cores of queries is a sufficient and necessary condition for equivalence of conjunctive queries with comparisons similar to the classical relational setting. However, it is not a necessary condition for equivalence of count-distinct queries. We introduce a relaxation of this condition based on a new notion, which is a potentially new query equivalent to the initial query, introduced to capture the behavior of countdistinct operator.

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Equivalences among aggregate queries with negation

Cited by 24 publications

References 17 publications

Explaining Wrong Queries Using Small Examples

Explaining Wrong Queries Using Small Examples

SPORES: Sum-Product Optimization via Relational Equality Saturation for Large Scale Linear Algebra

Decidability of Equivalence of Aggregate Count-Distinct Queries

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