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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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Please answer all questions will give rating surely
![Recall that the set {0,1}* is the set of finite length bit strings defined recursively by the
following rules:
Foundation rule: The empty string A E {0,1}*.
Constructor rule: For s E {0,1}*, s1 E {0,1}* and s0 E {0,1}*.
Consider the recursive function flip which takes a bit strings for input and gives a bit
strings as output, defined by the following:
Foundation rule: flip(^) = \.
%3D
Constructor rule: For s E {0,1}*, flip(sO) = flip( s )1 and flip( s 0) = flip( s )1.
%3D
а.
What is the output when flip is applied to the following strings? For full-
credit, you must show the step-by-step application of the flip function.
i. 010
ii. 1101
iii. 0010
Use structural induction to show that flip(flip(s)) = s for any s E {0,1}*.
%3D
b.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fac74fb84-3cf7-42dc-91d6-acc9f04e40e8%2Fe3913fc2-96d3-432c-8d90-bf622327bf5f%2F37ssok_processed.png&w=3840&q=75)
Transcribed Image Text:Recall that the set {0,1}* is the set of finite length bit strings defined recursively by the
following rules:
Foundation rule: The empty string A E {0,1}*.
Constructor rule: For s E {0,1}*, s1 E {0,1}* and s0 E {0,1}*.
Consider the recursive function flip which takes a bit strings for input and gives a bit
strings as output, defined by the following:
Foundation rule: flip(^) = \.
%3D
Constructor rule: For s E {0,1}*, flip(sO) = flip( s )1 and flip( s 0) = flip( s )1.
%3D
а.
What is the output when flip is applied to the following strings? For full-
credit, you must show the step-by-step application of the flip function.
i. 010
ii. 1101
iii. 0010
Use structural induction to show that flip(flip(s)) = s for any s E {0,1}*.
%3D
b.
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