# P=BPP and derandomizing Vazirani-Valiant?

Vazirani-Valiant reduction is a randomized reduction from $$SAT$$ to unambiguous $$SAT$$.

1. Is $$P=BPP$$ strong enough to derandomize Vazirani-Valiant reduction?

2. If not what other ingredients are necessary to derandomize Vazirani-Valiant reduction?

The above two are addressed in Derandomizing Valiant-Vazirani?. However we can still ask whether there is a possibility of $$P$$ is not $$BPP$$ and still if it would be possible to derandomize Vazirani-Valiant.

1. Is $$P=BPP$$ necessary to derandomize Vazirani-Valiant reduction?

2. If not what would derandomizing Vazirani-Valiant reduction tell about $$P=BPP$$?

• The following question might be helpful: cstheory.stackexchange.com/questions/7552/… – Or Meir Apr 27 '17 at 21:57
• I believe 1 and 2 are basically a duplicate of the question Or pointed to, and are essentially answered there. I suggest to focus the question down to 3 and 4, and just point out as background that the other question essentially answers the opposite direction. – Joshua Grochow Apr 28 '17 at 3:31
• @JoshuaGrochow ok I will update. – Turbo Apr 28 '17 at 16:55