Can a NP-complete language be P-immune?

Why can't existence of P-immune languages separate NP from P?


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Assuming that

  • pseudorandom generators and secure one‐way permutations exist,

it follows that

  • $\mathsf{NP}$‐complete sets are not $\mathsf P$‐immune.

Christian Glaßer, A. Pavan, Alan L. Selman, and Samik Sengupta, Properties of NP‐Complete Sets SIAM J. Comput., 36(2), 516–542, 2006.


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