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    $\begingroup$ "Without fully simulating any string" is something that is far, far away from well-defined. Can you define it formally, i.e., using mathematical terms? I would bet, either you can, in which case the answer should become obvious or you cannot. In that sense, the first question should be "how to define 'without fully simulating any string'"? $\endgroup$ Commented Mar 9, 2019 at 20:49
  • $\begingroup$ @Apass.Jack Thank you for the helpful comment, I have edited the question to be more well-defined, can you take a look? $\endgroup$ Commented Mar 10, 2019 at 9:08
  • $\begingroup$ Do not put "edit" sections after your original question. Instead, modify the question so that it reads the way you think it should. $\endgroup$ Commented Mar 10, 2019 at 11:05