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Maybe an answer to this

Here input of length and position is binary rather than unary, so traditional "DLOGTIME-uniform" is now "O(n)-uniform". (If traditional "DLOGTIME-uniform" already take binary input then this question has false assumption)

Surely O(n) isn't that low, so will a lower model lead to weaker result? E.g. is uniformNC∩O(n)-uniform AC0 weaker than uniform AC0?

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  • $\begingroup$ What exactly is your question? $\endgroup$ Dec 29, 2022 at 18:46
  • $\begingroup$ @EmilJeřábek will a lower model(e.g. uniformNC-uniform) lead to weaker result? $\endgroup$
    – l4m2
    Dec 30, 2022 at 1:58
  • $\begingroup$ What "result"?? $\endgroup$ Dec 30, 2022 at 8:28
  • $\begingroup$ Also, if you consider the input as indices written in binary, then DLOGTIME-uniformity becomes linear-time uniformity rather than polynomial-time uniformity. It is actually already defined that way; it is only called DLOGTIME-uniform in reference to the input size of the circuit being uniformized. $\endgroup$ Dec 30, 2022 at 8:33
  • $\begingroup$ @EmilJeřábek The ability it constructs circuit $\endgroup$
    – l4m2
    Dec 30, 2022 at 9:33

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