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 Jun 26 comment Isomorphic encryption or homomorphic encryption? A set endowed with an operation possesses an algebraic structure, even if the structure is not a group. We are sure that the set M is closed under *, otherwise, the "multiplication of two valid plaintexts will not result in a valid plaintext. So, in the very least, we have an algebraic structure called Magma: en.wikipedia.org/wiki/Magma_(algebra). Mar 12 awarded Notable Question Feb 11 comment Solve by induction: $n!>(n/e)^n$ Related question: math.stackexchange.com/q/144176/2420 Dec 20 awarded Constituent Dec 9 awarded Caucus Dec 1 awarded Altruist Nov 30 comment Understanding the complexity class $P^O$ for randomized oracles Oh, I see. Thanks for the magical explanation, it's now crystal clear :) Nov 30 comment Understanding the complexity class $P^O$ for randomized oracles I believe $M$ cannot simply return the answer of the $BPP$ oracle. For the oracle, it is acceptable if it decides the language membership with probability better than (say) 2/3. However, the deterministic machine $M$ should "perfectly" decide the membership: It should output 1 if and only if the input belongs to some language. Nov 30 comment Understanding the complexity class $P^O$ for randomized oracles Please clarify this point: $M^O$ is a deterministic machine if $M$ is a deterministic machine. So, shouldn't $P^{BPP}$ be a deterministic complexity class? Nov 26 awarded Investor Oct 11 awarded Yearling Jul 2 awarded Curious May 24 answered what is the relationship between the complexity class E(and EXP) and NP? May 7 awarded Notable Question Feb 16 awarded Good Question Nov 16 awarded Popular Question Nov 3 awarded Nice Question Oct 11 awarded Yearling Sep 23 asked A tight lower bound for the entropy of the XOR of two random variables Sep 8 awarded Popular Question