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I wrote the following table for all the closures in those classes.

is anything there incorrect?

also, would appreciate help with coNP and coRE closures. couldn't find much information about it online.

enter image description here

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  • $\begingroup$ I believe RE is closed under reversal, if that's what $A^R$ means. Can't you just the reverse input before running the original algorithm? Additionally, for $A\triangle B$ I believe it's unknown whether NP is closed to it, since it is if $P = NP$ and isn't if $NP \neq coNP$ $\endgroup$ Commented Jun 6, 2023 at 13:06
  • $\begingroup$ @CommandMaster thanks, I missed the reversal of RE, you're right. $\endgroup$
    – Skynet
    Commented Jun 6, 2023 at 13:35

1 Answer 1

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updated table:

enter image description here

"?" means it's an open question (unkonwn)

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