Granularity of Parallel Memories

Kurt Mehlhorn

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Ks before, let r(x) = x mod m and H^ = {roh; h e H^}.
Before we analyze the behavior of class H^ we show that elements of H^ are easy to find by a probabilistic algorithm. More precisely, we show that a significant fraction of all (0, 1 )-matrices is invertible.
2 Lemm 1; JH^] = n (2"-2^) > 2^" >/e^^^ 0 e i=l i=l n -(7/5) I 2"i > e 1=1 since In(l-x) > -7x/5 for (Xx e Lemma 1 shows that at least 2 5% of all (0, 1 )-matrices are Invertible. Hence invertible (0, 1 )-matrices can be found... by taking a few random (0, l)-ma trices and checking for singularity by Gaussian elimination.

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