Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider the question whether two queries to SAT are as porful as one query.  show that if P/sup NP[1]/=P/sup NP[2]/ then; locally either NP=coNP or NP has polynomial-size circuits; P/sup NP/=P/sup NP[1]/; /spl Sigma//sub 2//sup p/=UP/sup NP[1]//spl cap/RP/sup NP[1]/; PH=BPP/sup NP[1]/. Moreover  extend work of E. Hemaspaandra et al. (1997) to show that if P(/spl Sigma//sub 2//sup p/[1])=P(/spl Sigma//sub 2//sup p/[2]) then /spl Sigma//sub 2//sup p/=/spl Pi//sub 2//sup p/.  also give a relativized world where P/sup NP[1]/=P/sup NP[2]/ but NP/spl ne/coNP.
['Harry Buhrman', 'Lance Fortnow']
I am writing a research paper on a idea Two queries
[{"from": "human", "value": "I am writing a research paper on a idea Two queries"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider the question whether two queries to SAT are as porful as one query.  show that if P/sup NP[1]/=P/sup NP[2]/ then; locally either NP=coNP or NP has polynomial-size circuits; P/sup NP/=P/sup NP[1]/; /spl Sigma//sub 2//sup p/=UP/sup NP[1]//spl cap/RP/sup NP[1]/; PH=BPP/sup NP[1]/. Moreover  extend work of E. Hemaspaandra et al. (1997) to show that if P(/spl Sigma//sub 2//sup p/[1])=P(/spl Sigma//sub 2//sup p/[2]) then /spl Sigma//sub 2//sup p/=/spl Pi//sub 2//sup p/.  also give a relativized world where P/sup NP[1]/=P/sup NP[2]/ but NP/spl ne/coNP."}]