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Different Differences in Semirings

Author Dan Suciu

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OASIcs.Tannen.10.pdf
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  • 20 pages

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Subject Classification

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

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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.

Cite As Get BibTex

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

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.

References

  1. Mahmoud Abo Khamis, Hung Q. Ngo, Reinhard Pichler, Dan Suciu, and Yisu Remy Wang. Convergence of datalog over (pre-) semirings. In Leonid Libkin and Pablo Barceló, editors, PODS '22: International Conference on Management of Data, Philadelphia, PA, USA, June 12 - 17, 2022, pages 105-117. ACM, 2022. URL: https://doi.org/10.1145/3517804.3524140.
  2. P. J. Allen. A fundamental theorem of homomorphisms for semirings, 1969. URL: https://api.semanticscholar.org/CorpusID:8723880.
  3. K Amer. Equationally complete classes of commutative monoids with monus. Algebra Universalis, 18:129-131, 1984. URL: https://doi.org/10.1007/BF01182254.
  4. Yael Amsterdamer, Daniel Deutch, and Val Tannen. On the limitations of provenance for queries with difference. In Peter Buneman and Juliana Freire, editors, 3rd Workshop on the Theory and Practice of Provenance, TaPP'11, Heraklion, Crete, Greece, June 20-21, 2011. USENIX Association, 2011. URL: https://www.usenix.org/conference/tapp11/limitations-provenance-queries-difference.
  5. Bruno Bosbach. Komplementäre Halbgruppen. Ein Beitrag zur instruktiven Idealtheorie kommutativer Halbgruppen. Math. Annalen, 161:279-295, 1965. Google Scholar
  6. Stanley Burris and Hanamantagouda P. Sankappanavar. A course in universal algebra, volume 78 of Graduate texts in mathematics. Springer, 1981. Google Scholar
  7. Shumo Chu, Brendan Murphy, Jared Roesch, Alvin Cheung, and Dan Suciu. Axiomatic foundations and algorithms for deciding semantic equivalences of SQL queries. Proc. VLDB Endow., 11(11):1482-1495, 2018. URL: https://doi.org/10.14778/3236187.3236200.
  8. Katrin M. Dannert, Erich Grädel, Matthias Naaf, and Val Tannen. Semiring provenance for fixed-point logic. In Christel Baier and Jean Goubault-Larrecq, editors, 29th EACSL Annual Conference on Computer Science Logic, CSL 2021, January 25-28, 2021, Ljubljana, Slovenia (Virtual Conference), volume 183 of LIPIcs, pages 17:1-17:22. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. URL: https://doi.org/10.4230/LIPIcs.CSL.2021.17.
  9. Floris Geerts and Antonella Poggi. On database query languages for k-relations. J. Appl. Log., 8(2):173-185, 2010. URL: https://doi.org/10.1016/j.jal.2009.09.001.
  10. Jonathan S Golan. Semirings and their Applications. Springer Science & Business Media, 2013. Google Scholar
  11. Erich Grädel and Val Tannen. Semiring provenance for first-order model checking. CoRR, abs/1712.01980, 2017. URL: https://arxiv.org/abs/1712.01980.
  12. Todd J. Green, Zachary G. Ives, and Val Tannen. Reconcilable differences. In Ronald Fagin, editor, Database Theory - ICDT 2009, 12th International Conference, St. Petersburg, Russia, March 23-25, 2009, Proceedings, volume 361 of ACM International Conference Proceeding Series, pages 212-224. ACM, 2009. URL: https://doi.org/10.1145/1514894.1514920.
  13. Todd J. Green, Gregory Karvounarakis, and Val Tannen. Provenance semirings. In Leonid Libkin, editor, Proceedings of the Twenty-Sixth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, June 11-13, 2007, Beijing, China, pages 31-40. ACM, 2007. URL: https://doi.org/10.1145/1265530.1265535.
  14. M. Henriksen. Ideals in semirings with commutative addition. Notices of the American Mathematical Society, 6:321, 1958. Google Scholar
  15. D. R. Latorre. A note on quotient semirings. Proceedings of the American Mathematical Society, 24(3):463-465, 1970. URL: http://www.jstor.org/stable/2037388.
  16. M. Sen and Mahim Adhikari. On k-ideals of semirings. International Journal of Mathematics and Mathematical Sciences, 15, January 1992. URL: https://doi.org/10.1155/S0161171292000437.
  17. Edward Szpilrajn. Sur l'extension de l'ordre partiel. Fundamenta Mathematicae, 16(1):386-389, 1930. URL: http://eudml.org/doc/212499.
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