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I was reading https://www2.cs.duke.edu/courses/spring02/cps296.1/lectures/08-view.pdf

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Or in the paper "Incremental Maintenance of Views with Duplicates," by Griffin and Libkin, SIGMOD, 1995. figure 2. enter image description here

I don't understand why we need to min(R,ΔR) before -. Is there any counterexample?

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Just realize the reason after posting the question. Counterexample: R =

A B

1 2

1 1

1 1

ΔR =

A B

1 1

1 1

1 1

Assume we want ΠA(R - ΔR)

The true answer is first R - ΔR:

A B

1 2

Then project A:

A

1

However, if ΠA(R - ΔR) = ΠA(R) - ΠA(ΔR). ΠA(R):

A

1

1

1

ΠA(ΔR):

A

1

1

1

ΠA(R) - ΠA(ΔR) = ∅

ΠA(R - ΔR) = ΠA(R) - ΠA(R min ΔR).

R min ΔR:

A B

1 1

1 1

ΠA(R min ΔR):

A

1

1

ΠA(R) - ΠA(R min ΔR):

A

1

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    $\begingroup$ This is not clear, why did you write these things & how is it an answer? PS Please read the edit help re line breaks. PS Please use text, not images, for what can be given in text. Explain how what you quote has to do with your post, don't expect us to read an entire reference or figure out what about it has what to do with your post or what its notation means. $\endgroup$
    – philipxy
    Aug 24, 2021 at 1:31

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