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Parallel Prefix Computation
 Journal of the ACM
, 1980
"... ABSTRACT The prefix problem is to compute all the products x t o x2.... o xk for i ~ k. ~ n, where o is an associative operation A recurstve construction IS used to obtain a product circuit for solving the prefix problem which has depth exactly [log:n] and size bounded by 4n An application yields fa ..."
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ABSTRACT The prefix problem is to compute all the products x t o x2.... o xk for i ~ k. ~ n, where o is an associative operation A recurstve construction IS used to obtain a product circuit for solving the prefix problem which has depth exactly [log:n] and size bounded by 4n An application yields fast, small Boolean ctrcmts to simulate fimtestate transducers. By simulating a sequentml adder, a Boolean clrcmt which has depth 2[Iog2n] + 2 and size bounded by 14n Is obtained for nbit binary addmon The size can be decreased significantly by permitting the depth to increase by an addmve constant
The History and Status of the P versus NP Question
, 1992
"... this article, I have attempted to organize and describe this literature, including an occasional opinion about the most fruitful directions, but no technical details. In the first half of this century, work on the power of formal systems led to the formalization of the notion of algorithm and the re ..."
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Cited by 60 (1 self)
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this article, I have attempted to organize and describe this literature, including an occasional opinion about the most fruitful directions, but no technical details. In the first half of this century, work on the power of formal systems led to the formalization of the notion of algorithm and the realization that certain problems are algorithmically unsolvable. At around this time, forerunners of the programmable computing machine were beginning to appear. As mathematicians contemplated the practical capabilities and limitations of such devices, computational complexity theory emerged from the theory of algorithmic unsolvability. Early on, a particular type of computational task became evident, where one is seeking an object which lies
Probabilistic Parallel Prefix Computation
, 1993
"... Given inputs x,..., xn, which are independent identically distributed random variables over a domain D, and an associative operation o, the probabilistic prefix computation problem is to compute the product x o x2 o .. o xn and its n  1 prefixes. Instances of this problem are finite state transd ..."
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Given inputs x,..., xn, which are independent identically distributed random variables over a domain D, and an associative operation o, the probabilistic prefix computation problem is to compute the product x o x2 o .. o xn and its n  1 prefixes. Instances of this problem are finite state transductions on random inputs, the addition or subtraction of two random nbit binary numbers, and the multiplication or division of a random nbit binary number by a constant.