SPES: A Two-Stage Query Equivalence Verifier
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In database-as-a-service platforms, automated verification of query equivalence helps eliminate redundant computation across queries (i.e., overlapping sub-queries). State-of-the-art tools for automated detection of query equivalence adopt two different approaches. The first technique is based on reducing queries to algebraic expressions and proving their equivalence using an algebraic theory. The limitations of this approach are threefold. It cannot prove the equivalence of queries with significant differences in the attributes of their relational operators. It does not support certain widely-used SQL features. Its verification procedure is computationally intensive. The second technique is based on deriving the symbolic representation of the queries and proving their equivalence using the satisfiability modulo theory. The limitations of this approach are twofold. It only proves equivalence of queries under set semantics. It cannot prove the equivalence of queries with significant structural differences in their abstract syntax trees. In this paper, we present a novel two-stage approach to automated verification of query equivalence that addresses the limitations of these individual techniques. The first stage consists of reducing queries to a novel algebraic representation and then normalizing the resulting algebraic expressions to minimize structural differences. The second stage consists of applying a verification algorithm to convert the normalized algebraic expressions to a novel query pair symbolic representation and proving their equivalence under bag semantics using satisfiability modulo theory. We implement our two-stage approach in SPES. SPES proves the equivalence of a larger set of query pairs (90/232) under bag semantics compared to the state-of-the-art tools based on algebraic (30/232) under bag semantics and symbolic approaches (67/232) under set semantics.
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