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- W1970452008 abstract "We consider the computation of finite semigroups using unbounded fan-in circuits. There are constant-depth, polynomial size circuits for semigroup product iff the semigroup does not contain a nontrivial group as a subset. In the case that the semigroup in fact does not contain a group, then for any primitive recursive function f, circuits of size O(nf−1(n)) and constant depth exist for the semigroup product of n elements. The depth depends upon the choice of the primitive recursive function f. The circuits not only compute the semigroup product, but every prefix of the semigroup product. A consequence is that the same bounds apply for circuits computing the sum of two n-bit numbers." @default.
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- W1970452008 date "1983-01-01" @default.
- W1970452008 modified "2023-09-26" @default.
- W1970452008 title "Unbounded fan-in circuits and associative functions" @default.
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- W1970452008 doi "https://doi.org/10.1145/800061.808732" @default.
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