Ieee Transactions on Computers , July 1970
نویسندگان
چکیده
von Neumann [2], Codd [4], and others who attempt to achieve various computational goals using minimal (for example, fewest states) primitive modules. Input and output are all done from a single machine, which, while no theoretical limitation because of the lumping of finite-state machines, is a further dissimilarity between the author's arrays and practical parallel-processing computing schemes. Together, the results on the hierarchy (based on dimension) and the power of arrays with a simple stencil (only nearest neighbors) constitute a principle that having an extra dimension available is more powerful than merely having a broader reach in fewer dimensions. It might be interesting to see how this principle would be affected by placing various restrictions on the classes of finite-state machines in the array. ERIK D. GOODMAN Logic of Computers Group University of Michigan Ann Arbor, Mich.
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On the Addition of Binary Numbers
An upper bound is derived for the time required to add numbers modulo 2n, using circuit elements with a limited fan-in and unit delay, and assuming that all numbers have the usual binary encoding. The upper bound is within a factor (1 + ε) of Winograd’s lower bound (which holds for all encodings), where ε → 0 as n → ∞, and only O(n log n) circuit elements are required. CommentsOnly the Abst...
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