Encyclopedia of Database Systems

2018 Edition
| Editors: Ling Liu, M. Tamer Özsu

Weak Equivalence

  • Christian S. JensenEmail author
  • Richard T. Snodgrass
Reference work entry
DOI: https://doi.org/10.1007/978-1-4614-8265-9_1533


Snapshot equivalence; Temporally weak


Informally, two tuples are snapshot equivalent or weakly equivalent if all pairs of timeslices with the same time instant parameter of the tuples are identical.

Let temporal relation schema R have n time dimensions, Di, i = 1,…, n, and let τ i, i = 1,…, n be corresponding timeslice operators, e.g., the valid timeslice and transaction timeslice operators. Then, formally, tuples x and y are weakly equivalent if
$$ \begin{aligned}&&\forall {t}_1\in {D}_1\dots \forall {t}_n\in {D}_n\left({\tau}_{t_n}^n\left(\dots \left({\tau}_{t_1}^1(x)\right.\right)\dots \right)\\&&{\quad}={\tau}_{t_n}^n\left(\dots \left(\left.{\tau}_{t_1}^1(y)\right)\dots \right)\right)\end{aligned} $$
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Recommended Reading

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    Aho AV, Sagiv Y, Ullman JD. Efficient optimization of a class of relational expressions. ACM Trans Database Syst. 1979;4(4):435–54.CrossRefGoogle Scholar
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    Aho AV, Sagiv Y, Ullman JD. Equivalences among relational expressions. SIAM J Comput. 1979;8(2):218–46.MathSciNetzbMATHCrossRefGoogle Scholar
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    Gadia SK. Weak temporal relations. In: Proceedings of the 4th ACM SIGACT-SIGMOD Symposium on Principles of Database Systems; 1985. p. 70–7.Google Scholar
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    Jensen CS, Dyreson CE, editors. A consensus glossary of temporal database concepts – February 1998 version. In: Etzion O, Jajodia S, Sripada S, editors. Temporal databases: research and practice, LNCS 1399. Berlin: Springer; 1998. p. 367–405.Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Computer ScienceAalborg UniversityAalborgDenmark
  2. 2.Department of Computer ScienceUniversity of ArizonaTucsonUSA
  3. 3.Dataware VenturesTucsonUSA

Section editors and affiliations

  • Richard T. Snodgrass
    • 1
  • Christian S. Jensen
    • 2
  1. 1.University of ArizonaTucsonUSA
  2. 2.Aalborg UniversityAalborg ØstDenmark