Shallow circuits and concise formulae for multiple addition and multiplication

@article{Paterson1993ShallowCA,
  title={Shallow circuits and concise formulae for multiple addition and multiplication},
  author={Mike Paterson and Uri Zwick},
  journal={computational complexity},
  year={1993},
  volume={3},
  pages={262-291}
}
A theory is developed for the construction of carry-save networks with minimal delay, using a given collection of carry-save adders each of which may receive inputs and produce outputs using several different representation standards. The construction of some new carry-save adders is described. Using these carry-save adders optimally, as prescribed by the above theory, we get {∧, ∨, ⊕}-circuits of depth 3.48 log2 n and {∧, ∨, ⌍}-circuits of depth 4.95 log2 n for the carry-save addition ofn… CONTINUE READING

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