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Compiling Existential Positive Queries to Bounded-Variable Fragments

Published: 25 June 2019 Publication History

Abstract

A crucial property of bounded-variable fragments of first-order logic is that they can be evaluated in polynomial time. It is therefore a useful preprocessing step to rewrite, if possible, a first-order query to a logically equivalent one with a minimum number of variables. However, it may occur that reducing the number of variables causes an increase in formula size. We investigate this trade-off for the existential-positive fragment of first-order queries, where variable minimisation is decidable in general. In particular, we study the blow-up in the formula size when compiling existential-positive queries to the bounded variable fragment of positive first-order logic. While the increase of the formula size is always at most exponential, we identify situations (based on the signature and the number of variables) where only a polynomial blow-up is needed. In all other cases, we show that an exponential lower bound on the formula size of the compiled formula that matches the general upper bound. This exponential lower bound is unconditional, and is the first unconditional lower bound for formula size with respect to the studied compilation; it is proved via establishing a novel interface with circuit complexity which may be of future interest.

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cover image ACM Conferences
PODS '19: Proceedings of the 38th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems
June 2019
494 pages
ISBN:9781450362276
DOI:10.1145/3294052
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 25 June 2019

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Author Tags

  1. bounded-variable logic
  2. compilation
  3. existential positive queries
  4. parameterized complexity

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  • Research-article

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  • Ministerio de Educación, Cultura y Deporte
  • Deutsche Forschungsgemeinschaft

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SIGMOD/PODS '19
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SIGMOD/PODS '19: International Conference on Management of Data
June 30 - July 5, 2019
Amsterdam, Netherlands

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PODS '19 Paper Acceptance Rate 29 of 87 submissions, 33%;
Overall Acceptance Rate 642 of 2,707 submissions, 24%

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