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We establish a pumping lemma for real-time deterministic context-free languages. The pumping lemma is useful to prove that a given deterministic context-free language is not real-time. The proving scheme by the pumping lemma is shown by...

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The Moore–Penrose inverse A+ of a block circulant matrix whose blocks are arbitrary square matrices is obtained. An explicit form is given for A+ in terms of the blocks of A. The eigenvalues of A are determined in terms of the eigenva...

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