1. Given a Boolean function f : {0,1}" → {0, 1} and a boolean circuit C of size |C| = s that computes f, show that there exists a boolean circuit C' such that: (a) C' computes f, (b) |C'| < 2s + n, and, (c) All - gates are next to the input gates. The rest of the circuit contains only A, V gates.

1. Given a Boolean function f : {0,1}" → {0, 1} and a boolean circuit C of size |C| = s that computes f, show that there exists a boolean circuit C' such that: (a) C' computes f, (b) |C'| < 2s + n, and, (c) All - gates are next to the input gates. The rest of the circuit contains only A, V gates.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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1. Given a Boolean function f : {0, 1}" → {0,1} and a boolean circuit C of size
|C|
= s that computes f, show that there exists a boolean circuit C' such
that:
(a) C' computes f,
(b) |C'| < 2s + n, and,
(c) All - gates are next to the input gates. The rest of the circuit contains
only ^, V gates.

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