A logarithmic time sort for linear size networks
Journal of the ACM (JACM)
Sorting in c log n parallel steps
Combinatorica
The circuit value problem is log space complete for P
ACM SIGACT News
The construction of Huffman-equivalent prefix code in NC
ACM SIGACT News
Generalized sweep methods for parallel computational geometry
SPAA '90 Proceedings of the second annual ACM symposium on Parallel algorithms and architectures
Depth reduction for noncommutative arithmetic circuits
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Towards automatic parallelization of tree reductions in dynamic programming
Proceedings of the eighteenth annual ACM symposium on Parallelism in algorithms and architectures
On unlimited parallelism of DSP arithmetic computations
ICASSP'93 Proceedings of the 1993 IEEE international conference on Acoustics, speech, and signal processing: plenary, special, audio, underwater acoustics, VLSI, neural networks - Volume I
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The dynamic parallel complexity of general computational circuits (defined in introduction) is discussed. We exhibit some relationships between parallel circuit evaluation and some uniform closure properties of a certain class of unary functions and present a systematic method for the design of processor efficient parallel algorithms for circuit evaluation. Using this method: (1) we improve the algorithm for parallel Boolean circuit evaluation; (2) we give a nontrivial upper bound for parallel min-max-plus circuit evaluation; (3) we partially answer the first open question raised in [MiRK85] by showing that all circuits over finite noncommutative semi-ring and circuits over infinite non-commutative semi-ring which has finite dimension over a commutative semi-ring can be evaluated in polylogarithmic time in its size and degree using M(n) processors. Moreover, we develop a theory for determining closure properties of certain classes of unary functions.