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Revision #1 to TR02-006 | 7th February 2002 00:00
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#### Random nondeterministic real functions and Arthur Merlin games Revision of: TR02-006

**Abstract:**
We construct a nondeterministic version of \textbf{APP}, denoted

\textbf{NAPP}, which is the set of all real valued functions

$f: \{ 0,1 \}^{*} \rightarrow [0,1]$, that are approximable within 1/$k$,

by a probabilistic nondeterministic transducer, in time poly($1^{k},n$).

We show that the subset of all Boolean functions in $\mbf{NAPP}$ is exactly

\textbf{AM}.

We exhibit a natural complete problem for \textbf{NAPP}, namely computing

the acceptance probability of a nondeterministic Boolean circuit.

Then we prove that similarly to \textbf{AM}, the error probability

for \textbf{NAPP} functions can be reduced exponentially.

We also give a co-nondeterministic version, denoted \textbf{coNAPP}, and prove

that all results for \textbf{NAPP} also hold for \textbf{coNAPP}.

Then we construct two mappings between \tbf{NAPP} and promise-\tbf{AM},

which preserve completeness.

Finally we show that in the world of deterministic computation, oracle access to

\textbf{AM} is the same as oracle access to \textbf{NAPP}, i.e.

$\mbf{P}^{\mbf{NAPP}} = \mbf{P}^{\mbf{prAM}}$.

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TR02-006 | 8th November 2001 00:00
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#### Random nondeterministic real functions and Arthur Merlin games

**Abstract:**
We construct a nondeterministic analogue to \textbf{APP}, denoted

\textbf{NAPP}; which is the set of all real valued functions

$f: \{ 0,1 \}^{*} \rightarrow [0,1]$, that are approximable within 1/$k$,

by a probabilistic nondeterministic transducer, in time poly($n,1^{k}$).

We show that the subset of all Boolean functions in $\mbf{NAPP}$ is exactly

\textbf{AM}.

We exhibit a natural complete problem for \textbf{NAPP}, namely computing

the acceptance probability of a nondeterministic Boolean circuit.

Then we prove that similarly to \textbf{AM}, the error probability

for \textbf{NAPP} functions can be reduced exponentially.

We also give a co-nondeterministic version, denoted \textbf{coNAPP}, and prove

that all results for \textbf{NAPP} also hold for \textbf{coNAPP}.

Then we construct two mappings between \tbf{NAPP} and promise-\tbf{AM},

mapping complete problems to complete problems.

Finally we show that in the world of deterministic computation, oracle access to

\textbf{AM} is the same as oracle access to \textbf{NAPP}, i.e.

$\mbf{P}^{\mbf{NAPP}} = \mbf{P}^{\mbf{prAM}}$.