Question

(computability and complexity): prove well: if language A belongs to class BPP - then A ≤_P#SAT

Answer 1

#

A language A reduces to B in randomized polynomial-time, A ≤r B if there exists a polynomial-time probabilistic turing-machine M such that for all x ∈ {0, 1} ∗ :

Pr[B(M(x)) = A(x)] ≥ 2 3

Recall the reduction of P H to ⊕SAT.

#

A polynomial-time probabilistic turing-machine M works in space S(n) if for all input x ∈ {0, 1} ∗ and random strings r ∈ {0, 1} ∗ M(x, r) need work-space ≤ S(∣x∣).

A language L ∈ BP L if there exists a O(log(n))-space probabilistic turingmachine M such that ∀x:

Pr[M(x) = L(x)] ≥ 2 3

A language L ∈ RL if there exists a O(log(n))-space probabilistic turingmachine M such that ∀x:

x ∈ L ⇒ Pr[M(x) = 1] ≥ 2/3

x ≠ L ⇒ Pr[M(x) = 1] = 0

#

This is what i got fto prove from the Above Query.