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### Revision(s):

Revision #1 to TR02-006 | 7th February 2002 00:00

#### Random nondeterministic real functions and Arthur Merlin games Revision of: TR02-006

Revision #1
Authors: Philippe Moser
Accepted on: 7th February 2002 00:00
Keywords:

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

### Paper:

TR02-006 | 8th November 2001 00:00

#### Random nondeterministic real functions and Arthur Merlin games

TR02-006
Authors: Philippe Moser
Publication: 9th January 2002 21:27
Keywords:

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