A binary relation R ⊆ Σ∗ × Σ∗ is called polynomially honest if there exists a polynomial function p such that ⟨x, y⟩ ∈ R only if |x| ≤ p(|y|) and |y| ≤ p(|x|). A function f ∶ Σ∗ → Σ∗ is polynomially...


A binary relation R ⊆ Σ∗ × Σ∗ is called polynomially honest


if there exists a polynomial function p such that ⟨x, y⟩ ∈ R only if


|x| ≤ p(|y|) and |y| ≤ p(|x|). A function f ∶ Σ∗ → Σ∗ is polynomially honest if the relation {⟨x,f(x)⟩ ∶ x ∈ Σ∗} is polynomially honest. Prove that


A ⊆ Σ∗ is in NP if and only if A = Range(f) for some polynomially honest


function


f ∈ FP.



Jan 05, 2022
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