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Logical simpli cation is performed. using barcode integrating for none control to generate, create none image in none applications.generate qr code c# Appendix A Microsoft SQL Server int atoi(string& s) { int i, n, sign; / \(isdigit(s[0]))&&!(isdigit(s[1])); i = 0; sign = 1; n = 0; n = 10 * n + (s[i] 0 ); i = i + 1; return sign * n; }. int atoi(string& s) none none { int i, n, sign; / \(isdigit(s[0]))&&!(isdigit(s[1])); i = 0; sign = 1; n = 10 * 0 + (s[i] 0 ); i = i + 1; return sign * n; }. Corollary 3.10 is used to eliminate the assignment statement n = 0. int atoi(string& s) none none { int i, n, sign; / \(isdigit(s[0]))&&!(isdigit(s[1])); i = 0; n = (s[i] 0 ); sign = 1; i = i + 1; return sign * n; }. int atoi(string& s) { int i, n, sign; / \(isdigit(s[0]))&&!(isdigit(s[1])); i = 0; n = (s[i] 0 ); i = i + 1; sign = 1; return sign * n; }. Corollary 3.11 is applied to interchange the two statements. Appendix A int atoi(string& s) none none { int i, n, sign; / \(isdigit(s[0]))&&!(isdigit(s[1])); i = 0; n = (s[i] 0 ); i = i + 1; sign = 1; return sign * n; }. int atoi(string& s) { int i, n, sign; / \(isdigit(s[0]))&&!(isdigit(s[1])); i = 0; n = (s[i] 0 ); i = i + 1; return 1 * n; }. Corollary 3.13 is used in this step. int atoi(string& s) { int i, n, sign; / \(isdigit(s[0]))&&!(isdigit(s[1])); i = 0; n = (s[i] 0 ); i = i + 1; return n; }. int atoi(string& s) none none { int i, n, sign; / \(isdigit(s[0]))&&!(isdigit(s[1])); n = (s[0] 0 ); i = 0; i = i + 1; return n; }. Corollary 3.11 is applied here. Appendix A int atoi(string& s) { int i, n, sign; / \(isdigit(s[0]))&&!(isdigit(s[1])); n = (s[0] 0 ); i = 0; i = i + 1; return n; } } int atoi(string& s) { int i, n, sign; / \(isdigit(s[0]))&&!(isdigit(s[1])); n = (s[0] 0 ); i = 1; return n;. Corollary 3.10 is used to obtain this result. int atoi(string& s) { int i, n, sign; / \(isdigit(s[0]))&&!(isdigit(s[1])); n = (s[0] 0 ); i = 1; return n; }. int atoi(string& s) none none { int i, n, sign; / \(isdigit(s[0]))&&!(isdigit(s[1])); n = (s[0] 0 ); return n; i = 1; }. Corollary 3.13 is the basis for this transformation. int atoi(string& s) none none { int i, n, sign; / \(isdigit(s[0]))&&!(isdigit(s[1])); n = (s[0] 0 ); return n; }. int atoi(string& s) { int i, n, sign; / \(isdigit(s[0]))&&!(isdigit(s[1])); return (s[0] 0 ); n = (s[0] 0 ); }. Corollary 3.13 is applied in this step. Appendix A Thus we have shown that int atoi(string& s) { int i, n, sign; i = 0; / \!(isspace(s[i])); / \!(s[i] = = ); sign = 1; / \!(s[i] = = + . s[i] = = ); n = 0 none none ; / \ (isdigit(s[i])); n = 10 * n + (s[i] 0 ); i = i + 1; / \!(isdigit(s[i])); while (isdigit(s[i])) { n = 10 * n + (s[i] 0 ); i = i + 1; } return sign * n; }. int atoi(string& s) { int i, n, sign; / \(isdigit(s[0]))&&!(isdigit(s[1])); return (s[0] 0 ); }. Example A.2 To be analyzed is a C ++ program that computes the so called 91 function (Manna, 1974), which can be de ned as if x 100 then z := 91 else z := x - 10.. Appendix A Program A.2 #include <iostream none for none > using namespace std; int main() { int x, y, z; cin >> x; y = 1; while (x < = 100) { x = x + 11; y = y + 1; } while (y! = 1) { x = x 10; y = y 1; while (x < = 100) { x = x + 11; y = y + 1; } } z = x 10; cout << z = << z << endl; }. int main() { int x, y, z; cin >> x; y = 1; / \ x < = 100 x > 100; while (x none for none < = 100) { x = x + 11; y = y + 1; } while (y! = 1) { x = x 10; y = y 1; while (x < = 100) { x = x + 11; y = y + 1; } } z = x 10; cout << z = << z << endl; }. By virtue of Corollar y 4.8 we may insert a tautological constraint as shown on the right-hand side. Tautological constraints in a program allow us to simplify or to transform the program.

Therefore, as a general rule, we start by inserting as many tautological constraints as possible into part of the source code being examined. We then apply appropriate rules to rewrite the program. Once the rules have been applied, the tautological constraints will no longer be needed, and thus can be discarded.

For this reason, it is useful to mark a tautological constraint in some way (e.g., underline it in handwriting).

Henceforth a tautological constraint is given in italics..
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