In database-as-a-service platforms, automated ver-ification of query equivalence helps eliminate redundant computation in the form of overlapping sub-queries. Researchers have proposed two pragmatic techniques to tackle this problem. The first approach consists of reducing the queries to algebraic expressions and proving their equivalence using an algebraic theory. The limitations of this technique are threefold. It cannot prove the equivalence of queries with significant differences in the attributes of their relational operators (e.g., predicates in the filter operator). It does not support certain widely-used SQL features (e.g., NULL values). Its verification procedure is computationally intensive. The second approach transforms this problem to a constraint satisfaction problem and leverages a general-purpose solver to determine query equivalence. This technique consists of deriving the symbolic representation of the queries and proving their equivalence by determining the query containment relationship between the symbolic expressions. While the latter approach addresses all the limitations of the former technique, it only proves the equivalence of queries under set semantics (i.e., output tables must not contain duplicate tuples). However, in practice, database applications use bag semantics (i.e., output tables may contain duplicate tuples) In this paper, we introduce a novel symbolic approach for proving query equivalence under bag semantics. We transform the problem of proving query equivalence under bag semantics to that of proving the existence of a bijective, identity map between tuples returned by the queries on all valid inputs. We classify SQL queries into four categories, and propose a set of novel category-specific verification algorithms. We implement this symbolic approach in SPES and demonstrate that it proves the equivalence of a larger set of query pairs (95/232) under bag semantics compared to the SOTA tools based on algebraic (30/232) and symbolic approaches (67/232) under set and bag semantics, respectively. Furthermore, SPES is 3X faster than the symbolic tool that proves equivalence under set semantics.
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This content will become publicly available on May 10, 2025
From Shapley Value to Model Counting and Back
In this paper we investigate the problem of quantifying the contribution of each variable to the satisfying assignments of a Boolean function based on the Shapley value. Our main result is a polynomial-time equivalence between computing Shapley values and model counting for any class of Boolean functions that are closed under substitutions of variables with disjunctions of fresh variables. This result settles an open problem raised in prior work, which sought to connect the Shapley value computation to probabilistic query evaluation.
We show two applications of our result. First, the Shapley values can be computed in polynomial time over deterministic and decomposable circuits, since they are closed under OR-substitutions. Second, there is a polynomial-time equivalence between computing the Shapley value for the tuples contributing to the answer of a Boolean conjunctive query and counting the models in the lineage of the query. This equivalence allows us to immediately recover the dichotomy for Shapley value computation in case of self-join-free Boolean conjunctive queries; in particular, the hardness for non-hierarchical queries can now be shown using a simple reduction from the \#P-hard problem of model counting for lineage in positive bipartite disjunctive normal form.
more » « less- PAR ID:
- 10518839
- Publisher / Repository:
- ACM
- Date Published:
- Journal Name:
- Proceedings of the ACM on Management of Data
- Volume:
- 2
- Issue:
- 2
- ISSN:
- 2836-6573
- Page Range / eLocation ID:
- 1 to 23
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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