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    $\begingroup$ Is this bit equal to zero? $\endgroup$ Commented Mar 31, 2012 at 13:27
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    $\begingroup$ You have to explain "equivalent" in more detail, e.g. do you mean one can be solved using the other as an oracle/blackbox in polynomial time (or in logarithmic space)? Do you care about all problems or only problems inside $\sf{NP}$? $\endgroup$ Commented Mar 31, 2012 at 18:01
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    $\begingroup$ Depending on your viewpoint, the question is either trivial (take any decision problem that does not have a "$k$") or not answerable (how to prove that there "no equivalent opt. problem"?). $\endgroup$ Commented Apr 1, 2012 at 8:48