3. Let P: N→ N be a unary predicate (not necessarily computable). Define predicate Q: N → NbyQ(r)=1 if there are at least r natural numbers n such that P(n) = 10 otherwise.Show that is primitive recursive. (Hint: Let N be the number of natural numbers n such that1. Note that N is either infinity or some natural number; in any case N depends only on=P(n)P.)

To show that Q is primitive recursive, we need to define a primitive recursive function that…

3. Let P: N→ N be a unary predicate (not necessarily computable). Define predicate Q: N → N by Q(r) = = [1 if there are at least r natural numbers n such that P(n) = 1 { otherwise. Show that is primitive recursive. (Hint: Let N be the number of natural numbers n such that 1. Note that N is either infinity or some natural number; in any case N depends only on = P(n) P.)

3. Let P: N→ N be a unary predicate (not necessarily computable). Define predicate Q: N → N by Q(r) = = [1 if there are at least r natural numbers n such that P(n) = 1 { otherwise. Show that is primitive recursive. (Hint: Let N be the number of natural numbers n such that 1. Note that N is either infinity or some natural number; in any case N depends only on = P(n) P.)

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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Concept explainers

Randomized Select Algorithm

A randomized algorithm is defined as one that uses a certain amount of randomization in its logic or operation. It is said to be an algorithm that depends on the random number to perform its operation. It is used for reducing the overall time complexity, space complexity in the standard algorithm. The randomized algorithm uses the concept of random numbers to find the solutions to the different kinds of problems and also to improve the problem solutions.

Question

3. Let P: N→ N be a unary predicate (not necessarily computable). Define predicate Q: N → N
by
Q(r)
=
1 if there are at least r natural numbers n such that P(n) = 1
0 otherwise.
Show that is primitive recursive. (Hint: Let N be the number of natural numbers n such that
1. Note that N is either infinity or some natural number; in any case N depends only on
=
P(n)
P.)

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