Question: Prove that NPNP coNP = NP . Be sure you understand what this means. A language is in NPNP coNP if it can

Prove that NPNP

\

coNP

=

.

Be sure you understand what this means. A language is in NPNP

\

coNP if it can

be written in the form f

9

= 1

,

where

is a poly

-

time oracle TM

,

and

is a language

in NP

\

coNP. In other words,

has both an

-

style

algorithm and a

coNP

-

style

one. More formally,

there are polytime TMs

1

and

2

such that

=

9 1

1 1 = 1

=

8 2

2 2 = 1

.

Hint: compare the situation to NPNP or NPcoNP, both of which are equal to

\

Sigma

2 .

Think about where the

additional quantier comes from in these cases, and why you might not need one in our problem

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