Abstract
We show the following new lowness results for the probabilistic class ZPPNP.
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The class AM ∩ coAM is low for ZPPNP. As a consequence it follows that Graph Isomorphism and several group-theoretic problems known to be in AM ∩ coAM are low for ZPPNP.
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The class IP[P/poly], consisting of sets that have interactive proof systems with honest provers in P/poly, is also low for ZPPNP.
We consider lowness properties of nonuniform function classes, namely, NPMV/poly, NPSV/poly, NPMVt/poly, and NPSVt/poly. Specifically, we show that
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Sets whose characteristic functions are in NPSV/poly and that have program checkers (in the sense of [8]) are low for AM and ZPPNP.
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Sets whose characteristic functions are in NPMVt/poly are low for Σ p2
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Arvind, V., Köbler, J. (2000). Graph Isomorphism Is Low for ZPP(NP) and Other Lowness Results. In: Reichel, H., Tison, S. (eds) STACS 2000. STACS 2000. Lecture Notes in Computer Science, vol 1770. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46541-3_36
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DOI: https://doi.org/10.1007/3-540-46541-3_36
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