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
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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