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# lecture11 - A CIRCUIT CSci 5403 COMPLEXITY THEORY Is a...

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COMPLEXITY THEORY CSci 5403 LECTURE XI: PARALLEL COMPLEXITY A CIRCUIT Each node has a label 2 {x 1 ,…,x n , A , Ç , ¬ } ¬ x 0 x 1 x 2 A circuit C with n inputs and m outputs computes a function ƒ C : {0,1} n ! {0,1} m . Is a directed acyclic graph, where: Each node has in-degree either 0 (inputs), 1 ( ¬ ), or m ( A , Ç ) Nodes with out-degree 0 are the outputs of the circuit. Definition. A circuit family is a sequence of circuits C 1 , C 2 , C 3 , C 4 , … where for each n, C n has n inputs. We write the family as {C n } n 2 N . The language of a circuit family is the set L, where x 2 L , C |x| (x) = 1. The depth of a circuit depth(C) is the length of the longest path from an input gate to an output gate. A circuit family has depth f(n) if depth(C n ) f(n). What’s so interesting about depth? ¬ x 3 x 4 x 5 ¬ x 0 x 1 x 2 ¬ x 6 x 7 x 8 Gates can run in parallel! Then depth =

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## This note was uploaded on 10/21/2011 for the course CSCI 5403 taught by Professor Sturtivant,c during the Spring '08 term at Minnesota.

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lecture11 - A CIRCUIT CSci 5403 COMPLEXITY THEORY Is a...

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