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Different Differences in Semirings

Author Dan Suciu

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Author Details

Dan Suciu
  • University of Washington, Seattle, WA, USA

Funding

NSF-BSF 2109922, NSF IIS 2314527, NSF SHF 2312195.
  • Suciu, Dan: Partially Supported by NSF IIS 2314527.

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Dan Suciu. Different Differences in Semirings. In The Provenance of Elegance in Computation - Essays Dedicated to Val Tannen. Open Access Series in Informatics (OASIcs), Volume 119, pp. 10:1-10:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/OASIcs.Tannen.10

Abstract

Relational algebra operates over relations under either set semantics or bag semantics. In 2007 Val Tannen extended the semantics of relational algebra to K-relations, where each tuple is annotated with a value from a semiring. However, only the positive fragment of the relational algebra can be interpreted over K-relations. The reason is that a semiring contains only the operations addition and multiplication, and does not have a difference operation. This paper explores three ways of adding a difference operator to a semiring: as a freely generated algebra, by using the natural order, or by an explicit construction using products and quotients. The paper consists of both a survey of results from the literature, and of some novel results.

Subject Classification

ACM Subject Classification
  • Information systems → Structured Query Language
Keywords
  • Semirings
  • K-relations

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References

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