Oracle Separation of Complexity Classes and Lower Bounds for Perceptrons Solving Separation Problems
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چکیده
In the rst part of the paper we prove that, relative to a random oracle, the class NP has innnite sets having no innnite Co-NP-subsets (Co-NP-immune sets). In the second part we prove that perceptrons separating Boolean matrices in which each row has a one from matrices in which many rows (say 99% of them) have no ones must have large size or large order. This result partially strengthens one-in-a-box theorem by Minsky and Papert 16] stating that perceptrons of small order cannot decide if each row of given Boolean matrix has a one. As a consequence, we prove that AM \ Co-AM 6 6 PP under some oracle.
منابع مشابه
Lower Bounds for Perceptrons Solving some Separation Problems and Oracle Separation of AM from PP
We prove that perceptrons separating Boolean matrices in which each row has a one from matrices in which many rows have no one must have either large total weight or large order. This result extends one-in-a-box theorem by Minsky and Papert 13] stating that perceptrons of small order cannot decide if each row of a given Boolean matrix has a one. As a consequence, we prove that AM \ co-AM 6 6 PP...
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