Lower Bounds for Perceptrons Solving some Separation Problems and Oracle Separation of AM from PP
نویسنده
چکیده
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 under some oracle 1. This contrasts the fact that MA PP under any oracle.
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