Consider the following code, assuming that i, x, and n are integers, with n ≥ 0. • State a non-trivial loop invariant (which must include conditions for i and x). • Prove the loop invariant. Be sure that the proof includes the final conditions after the loop has ended. • Note: a correct proof of an incorrect invariant will still receive partial credit. Give the final value of x in terms of n. • Note: (for the sake of readability) the value 2² in the code below is 2 to the power of i. • Note: I or symbol (with ranges) meaning product or sum of terms can be used as part of loop invariant.

Consider the following code, assuming that i, x, and n are integers, with n ≥ 0. • State a non-trivial loop invariant (which must include conditions for i and x). • Prove the loop invariant. Be sure that the proof includes the final conditions after the loop has ended. • Note: a correct proof of an incorrect invariant will still receive partial credit. Give the final value of x in terms of n. • Note: (for the sake of readability) the value 2² in the code below is 2 to the power of i. • Note: I or symbol (with ranges) meaning product or sum of terms can be used as part of loop invariant.

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

Computational Systems

The computation systems can be defined as the systems that are capable of solving a problem that includes calculations either mathematical or logical, and are able to produce the result as an output. For example, a simple calculator that is given a set of numbers and operators as input and produces the result as an output can be defined as a computational system. The above example is a simple illustration only, the computational systems range from simple devices to complex devices such as the systems that control the SpaceX companies, Starlink satellites which are being quite recently seen in the skies at many places globally.

Question

Not part of an assignment, just want to understand the topic better

Consider the following code, assuming that i, x, and n are integers, with n ≥ 0.
State a non-trivial loop invariant (which must include conditions for i and x).
Prove the loop invariant. Be sure that the proof includes the final conditions after the loop has ended.
Note: a correct proof of an incorrect invariant will still receive partial credit.
Give the final value of x in terms of n.
Note: (for the sake of readability) the value 2² in the code below is 2 to the power of i.
Note: I or symbol (with ranges) meaning product or sum of terms can be used as part of loop invariant.
i = 0;
x = 1;
//
while in do
//
//
i=i+1;
//
X = X *
//
i;
X = X * 2¹;
//
After the loop, x =
(the invariant goes here)

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