Abstract
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(n 2) gates and O(nm 3 + n 3 m) wires) and for the multiplication of two n-bit numbers in depth 4 (O(n 2) gates and O(n 4) wires) are presented.
Supported by DFG Grant No. We 1066 / 2 - 1.
Supported by DFG Grant No. Me 872 / 1 - 2.
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© 1991 Springer-Verlag Berlin Heidelberg
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Hofmeister, T., Hohberg, W., Köhling, S. (1991). Some notes on threshold circuits, and multiplication in depth 4. In: Budach, L. (eds) Fundamentals of Computation Theory. FCT 1991. Lecture Notes in Computer Science, vol 529. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54458-5_67
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DOI: https://doi.org/10.1007/3-540-54458-5_67
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