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I think the notion you're looking for is differing-inputs indistinguishability obfuscation(diO), or originally called extractability iO: https://eprint.iacr.org/2013/650.pdf The definition of diO tells us: if there's a non-uniform PPT adversary that can distinguish the obfuscations of two circuits with "almost same" functionalities Obf($C_1$) and Obf($C_2$),...


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