On the Depth Complexity of the Counting Functions
نویسنده
چکیده
We use Karchmer and Wigderson’s recent characterization of circuit depth in terms of communication complexity to design shallow Boolean circuits for the counting functions. We show that the MOD, counting function on n arguments can be computed by Boolean networks which contain negations and binary ORand AND-gates in depth c logrn, where c A 2.881. This is an improvement over the obvious depth upper bound of 3 logan. We can also design circuits for the MOD, and MOD,, functions having depth 3.475 logan and 4.930 logan, respectively.
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عنوان ژورنال:
- Inf. Process. Lett.
دوره 35 شماره
صفحات -
تاریخ انتشار 1990