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Algorithmic Learning Theory analysis block Boolean Boolean circuits cache coherency controller communication complexity Computer Science consistent construct context-free grammars corresponding defined Definition delta networks denote derivation distributed edge eigenvectors error example exists Faculty of Engineering fault finite function gates given grammar graph IEEE IEICE implementation inference input Japan key words learning algorithm Lemma LOTOS matrix Member memory method neural network Nonmember obtained Occam algorithm operations optimal Osaka University output pair paper parallel parameters pattern languages performance polynomial problem Proc procedure Proof proposed protocol recognition regular language representation class respectively rule satisfies scheme Sect semantics sequence shown in Fig simulation string structure subcube symbol Technology Theorem theory tion Tohoku University Tokyo Trans translation tree pattern Turing machine Univ University of Tokyo variables vector