The OP didn’t ask what you can determine for a particular given finite time k. He asked if there is some finite way, period.
This is starting to remind me of wikipedia edit wars. I think it’s time to exit this conversation. OP’s question is answered, if he’s still interested.
You don’t need to do it for all N, just up to the N which the fake oracle is computing. Expected computational time for a randomly chosen N is infinite, but expected computation time for any -given- N is finite.
And only finite time is available- for most N, expected computation time is greater than available time; expected time is constant, and a finite number of N will have computation tine less than any C.
Now, do this in finite time for all N without knowing N.
This procedure works for all finite N, without knowing what N is. I am confused by your comment.
Given finite time, there is a maximum N that you can test.
The OP didn’t ask what you can determine for a particular given finite time k. He asked if there is some finite way, period.
This is starting to remind me of wikipedia edit wars. I think it’s time to exit this conversation. OP’s question is answered, if he’s still interested.
You don’t need to do it for all N, just up to the N which the fake oracle is computing. Expected computational time for a randomly chosen N is infinite, but expected computation time for any -given- N is finite.
And only finite time is available- for most N, expected computation time is greater than available time; expected time is constant, and a finite number of N will have computation tine less than any C.