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- W2068154147 abstract "We establish connections between parallel circuit evaluation and uniform algebraic closure properties of unary function classes. We use this connection in the development of time-efficient and processor-efficient parallel algorithms for the evaluation of algebraic circuits. Our algorithm provides a nontrivial upper bound on the parallel complexity of the circuit value problem over ${{Bbb R},min,max,+}$ and ${{Bbb R}^{+},min,max,times}$. We partially answer an open question of Miller, Ramachandran, and Kaltofen by showing that circuits over a polynomial-bounded noncommutative semiring and circuits over infinite noncommutative semirings with a polynomial-bounded dimension over a commutative semiring can be evaluated in polylogarithmic time in their size and degree using a polynomial number of processors. We also present an improved parallel algorithm for Boolean circuits." @default.
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- W2068154147 date "1999-01-01" @default.
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- W2068154147 title "The Dynamic Parallel Complexity of Computational Circuits" @default.
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- W2068154147 doi "https://doi.org/10.1137/s0097539795281724" @default.
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