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Probabilistic methods prove existence results in a nonconstructive fashion, by showing the chance of randomly selecting a solution is greater than zero.

33 votes
7 answers
2k views

List of proofs where existence through probabilistic method has not been constructivised

The probabilistic method as first pioneered by Erdős (although others have used this before) shows the existence of a certain object. What are some of the most important objects for which we can show …
3 votes
0 answers
240 views

Derandomization barriers in complexity theory applicable as barriers to constructive argumen...

The probabilistic method as first pioneered by Erdős (although others used this before) shows existence of a certain object while finding that object may take exponential time. (1) Is there any kn …
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