Nicholas Pippenger

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It is well known that time bounds for machines correspond closely to size bounds for networks, and that space bounds correspond to depth bounds. It is not known whether simultaneous time and space bounds correspond to simultaneous size and depth bounds. It is shown here that simultaneous time and "reversal" bounds correspond to simultaneous size and depth(More)
2. the sum of two (not necessarily distinct) previously computed vectors is available at a cost of one "step". (which can be regarded as integers); if we have no MULTIPLY instruction in our machine, we must simulate scalar multiplication by addition. (This problem would be more realistic if we allowed negative coefficients, subtractions, and short shifts.(More)
Systematic mistakes can be distinguished from other types of mistakes in that they are repeatable and predictable within a given organism, and are not due to uncertainty or lack of information. Here we provide a mathematical definition for the concept of systematic mistakes, which captures the way this concept has been used in the behavioral sciences. We(More)
Many behaviors have been attributed to internal conflict within the animal and human mind. However, internal conflict has not been reconciled with evolutionary principles, in that it appears maladaptive relative to a seamless decision-making process. We study this problem through a mathematical analysis of decision-making structures. We find that, under(More)
The assumption that different genetic elements can make separate contributions to the same quantitative trait was originally made in order to reconcile biometry and Mendelism and ever since has been used in population genetics, specifically for the trait of fitness. Here we show that sex is responsible for the existence of separate genetic effects on(More)
The problem solved in this paper is the following. Let x I' xn be indeterminates; let [I' ... , rk be simple radicals, by which is meant let rl' ... , rk be the square roots of rational functions of x I' ... , xn ; and let f I' , fm be simple algebraic Junctions, by which is meant let f I' , fm be rational functions of rl' ... , rk and xI' ... , x(l" What(More)
e _ 2'/z 2 4 4 6 6 8 1 / 8 2 () (33) 1/4 ( 5577) which is proved as follows . For v > 2, the Pth factor is [2' '. . 2P/(2p'+ 1) . (2 1)]'áz [(2"-'-1)!!z2"!!z/2 .2v-'!!z(2v-1)!!z]'/z where n!!=n(n-2) . . .4.2 if n is even, n(n-2) . . .3 .1 if n is odd. Since 2°!!=2 z " '2° '1 and (2°-1)!!=2°! /2°!!=2°!/2z" '2°'!, this expression becomes [2z"2°-'16/2 .2(More)
typedef struct { int owner; slock_t sem } Node; shared Node treee2*n-1]; shared T baggn], *result; shared int weighttn]; /* n>1 */ void process(pid) int pid; { int partner, son, node; node = pid; son = pid; while (node > 0) { son = node; node = (son) / 2; S_LOCK(&(treeenode].sem)); S_LOCK(&(treeeson].sem)); if (treeeson].owner != pid) { /* the son has(More)