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How Many Variables Are Needed to Express an Existential Positive Query?

Authors Simone Bova, Hubie Chen



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LIPIcs.ICDT.2017.9.pdf
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Simone Bova
Hubie Chen

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Simone Bova and Hubie Chen. How Many Variables Are Needed to Express an Existential Positive Query?. In 20th International Conference on Database Theory (ICDT 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 68, pp. 9:1-9:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)
https://doi.org/10.4230/LIPIcs.ICDT.2017.9

Abstract

The number of variables used by a first-order query is a fundamental measure which has been studied in numerous contexts, and which is known to be highly relevant to the task of query evaluation. In this article, we study this measure in the context of existential positive queries. Building on previous work, we present a combinatorial quantity defined on existential positive queries; we show that this quantity not only characterizes the minimum number of variables needed to express a given existential positive query by another existential positive query, but also that it characterizes the minimum number of variables needed to express a given existential positive query, over all first-order queries. Put differently and loosely, we show that for any existential positive query, no variables can ever be saved by moving out of existential positive logic to first-order logic. One component of this theorem’s proof is the construction of a winning strategy for a certain Ehrenfeucht-Fraiissé type game.
Keywords
  • existential positive queries
  • finite-variable logics
  • first-order logic
  • query optimization

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