Equivalences among aggregate queries with negation

  • Authors:

  • Sara Cohen;Werner Nutt;Yehoshua Sagiv

  • Affiliations:

  • Institute of Computer Science, The Hebrew University, Jerusalem 91904, Israel;Department of Computing and Electrical Engineering, Heriot-Watt University, Edinburgh EH14 4AS, Scotland, UK;Institute of Computer Science, The Hebrew University, Jerusalem 91904, Israel

  • Venue:
  • PODS '01 Proceedings of the twentieth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
  • Year:
  • 2001

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Abstract

Query equivalence is investigated for disjunctive aggregate queries with negated subgoals, constants and comparisons. A full characterization of equivalence is given for the aggregation functions count, max, sum, prod, top2 and parity. A related problem is that of determining, for a given natural number N, whether two given queries are equivalent over all databases with at most N constants. We call this problem bounded equivalence. A complete characterization of decidability of bounded equivalence is given. In particular, it is shown that this problem is decidable for all the above aggregation functions as well as for cntd (count distinct), stdev (standard deviation), median and avg. For quasilinear queries (i.e., queries in which predicates that occur positively are not repeated) it is shown that equivalence can be decided in polynomial time for the aggregation functions count, max, sum, prod, top2, parity, and avg. A similar result holds for cntd provided that a few additional conditions hold. The results are couched in terms of abstract characteristics of aggregation functions, and new proof techniques are used. Finally, the results presented also imply that equivalence, under bag-set semantics, is decidable for nonaggregate queries with negation.