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2 votes

What would $\mathcal{P} \neq \mathcal{NP}$ tell us about some non-constructive proofs?

I think you may need to formulate your question more precisely. Consider the following "nonconstructive proof": If you do blah-blah-blah and the result is 1 then YES, but if the result is 0 then NO, …
Timothy Chow's user avatar
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2 votes

Greedy euclidean tour expansion - a case of unexpected hanging?

There are many different ways of approaching the unexpected hanging paradox, some of which I describe in my paper on the subject, but I agree with Steven Landsburg that there is no useful sense in whi …
Timothy Chow's user avatar
  • 82.6k
11 votes

Is there a lower bound for the computational complexity of the traveling salesman problem?

There is a (nearly) trivial linear-time lower bound, because it takes linear time to read in the input. (I say this is nearly trivial because you do have to argue that it is necessary to examine at l …
Timothy Chow's user avatar
  • 82.6k