We present optimal depth Boolean circuits (depth O(log n)) for integer division, powering and multiple products We also show t h a t these three problems are of equivalent uniform depth and space complexity In addition, we describe an algorithm for testing drvisibility t h a t is optimal for both depth and space

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Abstract. We present optimal depth Boolean circuits (depth O(log n)) for integer division, powering, and multiple products. We also show that these three problems are of equivalent uniform depth and space complexity. In addition, we describe an algorithm for testing divisibility that is optimal for both depth and space.

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Algorithms are presented which modify logical networks of bounded fan-in to obtain functionally equivalent networks of bounded fan-m and fan-out, so that both size and depth are not increased by more than constant factors.