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If a polynomial-size pseudorandom generator G_k: {0,1}^k → {0,1}^{2k} has hardness H(G_k) ≥ 2^{k^ε} for some fixed ε > 0 and all sufficiently large k, then no P-natural property useful against P/poly exists.
Passage ID: pnp-entry-natural-proofs:v1
Source item: natural-proofs
Source record: pnp-rr@STOC-1994-author-paper
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Problem publication v14
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Proved
Established implication or scoped theorem in cited mathematics
A conditional barrier for this precise kind of circuit-lower-bound method; not for all mathematical proofs.
Observed Oct 10, 2026
History
Natural proofs connect lower bounds to pseudorandomness
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Manuscript / exposition · external
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Resource revision: STOC-1994-author-paper
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493cd619b123213f23de32f5075f34d30c563cbd562e025c99b0207568bc1c58Recorded authorship
Alexander Razborov · Steven Rudich
Alexander Razborov; Steven Rudich
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Razborov–Rudich · Natural proofs
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