Journal of the ACM (JACM)
Bounds on the time for parallel RAM's to compute simple functions
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
On non-linear lower bounds in computational complexity
STOC '75 Proceedings of seventh annual ACM symposium on Theory of computing
Two problems in concrete complexity: cycle detection and parallel prefix computation
Two problems in concrete complexity: cycle detection and parallel prefix computation
Counter-Free Automata (M.I.T. research monograph no. 65)
Counter-Free Automata (M.I.T. research monograph no. 65)
Finite monoids and the fine structure of NC1
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Size-time complexity of Boolean networks for prefix computations
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Size-time complexity of Boolean networks for prefix computations
Journal of the ACM (JACM)
Finite monoids and the fine structure of NC1
Journal of the ACM (JACM)
Parallel RAMs with bounded memory wordsize
SPAA '89 Proceedings of the first annual ACM symposium on Parallel algorithms and architectures
Tight bounds for the chaining problem
SPAA '91 Proceedings of the third annual ACM symposium on Parallel algorithms and architectures
Depth-Size Tradeoffs for Neural Computation
IEEE Transactions on Computers - Special issue on artificial neural networks
Deterministic restrictions in circuit complexity
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
On monotone formulae with restricted depth
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Superconcentrators, generalizers and generalized connectors with limited depth
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
The complexity of approximate counting
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
The complexity of computations by networks
IBM Journal of Research and Development - Mathematics and computing
Constant-Round Multiparty Computation for Interval Test, Equality Test, and Comparison
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Multiparty computation for interval, equality, and comparison without bit-decomposition protocol
PKC'07 Proceedings of the 10th international conference on Practice and theory in public-key cryptography
Quantum addition circuits and unbounded fan-out
Quantum Information & Computation
TCC'06 Proceedings of the Third conference on Theory of Cryptography
ASIACRYPT'11 Proceedings of the 17th international conference on The Theory and Application of Cryptology and Information Security
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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.