Homework Help is Here – Start Your Trial Now!
Engineering
Computer Science
2. Assume a declarative interface where n and max are constant integers, and A is an array of integers of size max. Consider the following correctness statement: ASSERT ( 1 < n <= max int i; i = n-1; A [n-1] = 1; while( i >= 1) { A[i-1] = A[i]ni + 1; i = i-1%; } ASSERT ForAll(k = 0%; k < n) A[k] == (n-k)* (n-k+1)/2) 1 (a) Give a complete proof tableau for the above correctness statement by adding all the intermediate assertions. State all the mathematical facts that are used in the proof. Hints: As our discussion in class will also emphasize the following two assertions are obvious tautologies: Forall (k=i; k Forall (k=i; k P(i) && Forall (k=i+1; k

2. Assume a declarative interface where n and max are constant integers, and A is an array of integers of size max. Consider the following correctness statement: ASSERT ( 1 < n <= max int i; i = n-1; A [n-1] = 1; while( i >= 1) { A[i-1] = A[i]ni + 1; i = i-1%; } ASSERT ForAll(k = 0%; k < n) A[k] == (n-k)* (n-k+1)/2) 1 (a) Give a complete proof tableau for the above correctness statement by adding all the intermediate assertions. State all the mathematical facts that are used in the proof. Hints: As our discussion in class will also emphasize the following two assertions are obvious tautologies: Forall (k=i; k Forall (k=i; k P(i) && Forall (k=i+1; k

Database System Concepts
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
See similar textbooks
icon
Related questions
Question
2. Assume a declarative interface where n and max are constant integers, and A is an array of integers of size max. Consider the following correctness statement: ASSERT ( 1 < n <= max int i; i = n-1; A [n-1] = 1; while( i >= 1) { A[i-1] = A[i]ni + 1; i = i-1%; } ASSERT ForAll(k = 0%; k < n) A[k] == (n-k)* (n-k+1)/2) 1 (a) Give a complete proof tableau for the above correctness statement by adding all the intermediate assertions. State all the mathematical facts that are used in the proof. Hints: As our discussion in class will also emphasize the following two assertions are obvious tautologies: Forall (k=i; k<j) P(k) <=> Forall (k=i; k<j) P(k) <=> P(i) && Forall (k=i+1; k<j) P(k) P(j-1) && Forall (k=i; k<j-1) P(k) That is, we can always separate as an extra conjunctive term an “end" of the range in a universally quantified property. Also note that this time the loop goes backward. This might be intimidating but actually that does not make much of a difference. (b) Provide a formal argument for the total correctness of the statement.
Transcribed Image Text:2. Assume a declarative interface where n and max are constant integers, and A is an array of integers of size max. Consider the following correctness statement: ASSERT ( 1 < n <= max int i; i = n-1; A [n-1] = 1; while( i >= 1) { A[i-1] = A[i]ni + 1; i = i-1%; } ASSERT ForAll(k = 0%; k < n) A[k] == (n-k)* (n-k+1)/2) 1 (a) Give a complete proof tableau for the above correctness statement by adding all the intermediate assertions. State all the mathematical facts that are used in the proof. Hints: As our discussion in class will also emphasize the following two assertions are obvious tautologies: Forall (k=i; k<j) P(k) <=> Forall (k=i; k<j) P(k) <=> P(i) && Forall (k=i+1; k<j) P(k) P(j-1) && Forall (k=i; k<j-1) P(k) That is, we can always separate as an extra conjunctive term an “end" of the range in a universally quantified property. Also note that this time the loop goes backward. This might be intimidating but actually that does not make much of a difference. (b) Provide a formal argument for the total correctness of the statement.
Expert Solution
steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
Recommended textbooks for you
Database System Concepts
Database System Concepts
Computer Science
ISBN:
9780078022159
Author:
Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:
McGraw-Hill Education
Starting Out with Python (4th Edition)
Starting Out with Python (4th Edition)
Computer Science
ISBN:
9780134444321
Author:
Tony Gaddis
Publisher:
PEARSON
Digital Fundamentals (11th Edition)
Digital Fundamentals (11th Edition)
Computer Science
ISBN:
9780132737968
Author:
Thomas L. Floyd
Publisher:
PEARSON
C How to Program (8th Edition)
C How to Program (8th Edition)
Computer Science
ISBN:
9780133976892
Author:
Paul J. Deitel, Harvey Deitel
Publisher:
PEARSON
Database Systems: Design, Implementation, & Manag…
Database Systems: Design, Implementation, & Manag…
Computer Science
ISBN:
9781337627900
Author:
Carlos Coronel, Steven Morris
Publisher:
Cengage Learning
Programmable Logic Controllers
Programmable Logic Controllers
Computer Science
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
SEE MORE TEXTBOOKS