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Let A = (aij) be a nonsingular n×n integer matrix such that log ∥A∥ ≤ no(1), $$\mathop {\max }\limits_{i,j}$$ |aij| ≤ ∥A∥ ≤ n $$\mathop {\max }\limits_{i,j}$$ |aij|. Then adj A, A−1 and all the coefficients of the characteristic polynomial of A including det A can be exactly evaluated on arithmetic circuits using O(log2n) parallel steps and M(n) processors where M(n) is the minimum number...
It is known that two n-bit numbers can be added by polynomial-size ∧- ∨-circuits of depth 3 [W2] and multiplied by threshold-circuits of depth 10. Two tricks for the reduction of depth in threshold circuits are formalized. Further, threshold circuits for the addition of m numbers of length n, m ≤ n, in depth 3 (with O(n2) gates and O(nm3 + n3m) wires) and...
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