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[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Software Engineering
[object Object],Build-and-Fix Write program Modify program Release
[object Object],Waterfall model Establish requirements Create  design Implement code Test system Release
[object Object],Iterative process Establish requirements Create  design Implement code Test system Release ,[object Object]
[object Object],Evolutionary Development Establish requirements Architectural  design Establish refinement scope System test Identify relationships Unit and Integration test Identify classes & objects Implementation Detailed  design Release Refinement cycle Specific methods and algorithms General structure of the system
[object Object],[object Object],[object Object],[object Object],Testing
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Testing (cont.)
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Testing (cont.)
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Functional Testing
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Unit Testing
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],White Box Testing
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Decision Coverage
[object Object],[object Object],[object Object],[object Object],Decision Coverage (cont.)
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Condition Coverage
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Condition Coverage (cont.)
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Multiple Condition Coverage
Multiple Condition Coverage (cont.) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],false false true false false true true true b == 0 a > 1 false false true false false true true true c > 1 a == 2
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Multiple Condition Coverage (cont.) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Multiple Condition Coverage (cont.)
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Gray Box Testing
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Equivalence Partitioning
[object Object],[object Object],[object Object],[object Object],[object Object],Equivalence Partitioning (cont.)
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Boundary Value Analysis
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Error Guessing
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Combined Strategy
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Testing Summary
[object Object],[object Object],[object Object],[object Object],[object Object],Testing  TrafficSignal
[object Object],Testing TrafficSignal (cont.) Left blank Left blank Dummy return value public class  TrafficSignal { public static final int  GREEN = 0; public static final int  YELLOW = 1; public static final int  RED = 2; private int  light; public  TrafficSignal () { } public int  light () { return  0; } public   void  change () { } }
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Testing  TrafficSignal  (cont.)
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Testing  TrafficSignal  (cont.)
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Testing  TrafficSignal  (cont.)
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Testing  TrafficSignal  (cont.)
Testing  TrafficSignal  (cont.)
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Testing  TrafficSignal  (cont.)
[object Object],[object Object],[object Object],Testing  TrafficSignal  (cont.)
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],/** ** ** @ensure  result == A * B **/ @require B >= 0 Verification ,[object Object],Is this method correct?
[object Object],[object Object],[object Object],Egyptian Numbering System
[object Object],[object Object],[object Object],Deciphering the Rhind Papyrus
1210554 Egyptian Multiplication 2468 490 4936 4936 245 9872 122 19744 19744 61 631808 631808 1 315904 315904 3 157952 157952 7 78976 78976 15 39488 30 1234 1234 981 Remainder “ Doubled” Multiplier “ Halved” Multiplicand
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],/** ** ** @ensure  result == A * B **/ @require B >= 0 Egyptian Multiplication (cont.)
[object Object],[object Object],[object Object],[object Object],Program Correctness
[object Object],[object Object],[object Object],Program Correctness (cont.)
[object Object],[object Object],[object Object],[object Object],Program Correctness (cont.)
[object Object],[object Object],[object Object],Program Correctness (cont.)
[object Object],[object Object],[object Object],Constructing Preconditions
[object Object],[object Object],[object Object],[object Object],[object Object],sum = 2 * x + 1; {sum > 1} Constructing Preconditions (cont.)
[object Object],[object Object],[object Object],The Assignment Axiom
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],a = b / 2 - 1; {a < 10} The Assignment Axiom (cont.)
[object Object],[object Object],[object Object],x = x - 3; {x > 0} The Assignment Axiom (cont.)
[object Object],[object Object],[object Object],[object Object],Sequential Statements
[object Object],[object Object],[object Object],[object Object],[object Object],y = 3 * x + 1; x = y + 3; {x < 10} Sequential Statements (cont.)
[object Object],[object Object],[object Object],[object Object],y = 3 * x + 1; {y < 7} Sequential Statements (cont.)
[object Object],[object Object],y = 3 * x + 1; x = y + 3; {x < 10} Sequential Statements (cont.) y = 3 * x + 1; {y < 7} x = y + 3; {x < 10} {x < 2} y = 3 * x + 1; {y < 7} x = y + 3; {x < 10}
[object Object],[object Object],[object Object],temp = x; x = y; y = temp; {x == b && y == a} Sequential Statements (cont.)
[object Object],temp = x; x = y; y = temp; {x == b && y == a} temp = x; x = y; {x == b && temp == a} y = temp; {x == b && y == a} temp = x; {y == b && temp == a} x = y; {x == b && temp == a} y = temp; {x == b && y == a} Sequential Statements (cont.) {y == b && x == a} temp = x; {y == b && temp == a} x = y; {x == b && temp == a} y = temp; {x == b && y == a} The constructed weakest precondition is: {y == b && x == a}   Comparing this with the postcondition, we see that the code does, indeed, swap the values of  x  and  y .
[object Object],[object Object],y = 4; z = x + y; {z = 7} y = 4; z = x + y; {z == 7} y = 4; {x + y == 7} z = x + y; {z == 7} {x + 4 == 7} y = 4; {x + y == 7} z = x + y; {z == 7} {x == 3} y = 4; {x + y == 7} z = x + y; {z == 7} The constructed weakest precondition is  {x == 3} .  Sequential Statements (cont.)
[object Object],{ P } if ( B ) {   S 1 } else {   S 2 } { Q } Conditional Statements
[object Object],[object Object],[object Object],[object Object],Conditional Statements (cont.)
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Conditional Statements (cont.)
[object Object],[object Object],[object Object],[object Object],Conditional Statements (cont.)
[object Object],if (x > y) { y = x - 1; } else { y = x + 1; } {y > 0} The  truecase : produces the precondition  {x – 1 > 0}  which simplifies to  {x > 1} . Backing over the  if  condition, we get  {(x > 1) && (x > y)} . y = x - 1; {y > 0} The  falsecase : produces the precondition  {x + 1 > 0}  which simplifies to  {x > -1} . Backing over the negative of the  if  condition, we get  {(x > -1) && (x <= y)} . y = x + 1; {y > 0} The disjoin of these is  {((x > 1) && (x > y)) || ((x > -1) && (x <= y))}  which serves as a precondition of the  if  structure.   Conditional Statements (cont.)
[object Object],if (n >= 5) { y = n * n; } else { y = n + 1; } {y == 36} The  truecase : produces the precondition  {n * n == 36}  which simplifies to  {n == 6 || n == -6} . Backing over the  if  condition, we get  {(n == 6 || n == -6) && (n >= 5)}  which simplifies to  {n == 6} . y = n * n; {y == 36} The  falsecase : produces the precondition  {n + 1 == 36}  which simplifies to  {n == 35} . Backing over the negtive of the  if  condition, we get  {(n == 35) && (n < 5)} . This is always false. y = n + 1; {y == 36} Thus, the constructed precondition is  {(n == 6) || false} , which simplifies to {n == 6} . Conditional Statements (cont.)
[object Object],[object Object],[object Object],if (x >= y) { max = x; } else { max = y; } Conditional Statements (cont.)
The  truecase : produces the precondition  {(x >= y && x == x) || (x < y && x == y)}   which simplifies to  {(x >= y && true) || false}  and further simplifies to  {x >= y} . Backing over the  if  condition, we get  {(x >= y) && (x >= y)}  which simplifies to  {x >= y} . max = x; {(x >= y && max == x) || (x < y && max == y)} if (x >= y) { max = x; } else { max = y; } {(x >= y && max == x) || (x < y && max == y)} Conditional Statements (cont.)
The  falsecase : produces the precondition  {(x >= y && y == x) || (x < y && y == y)}   which simplifies to  {(y == x) || (x < y && true)}  and further simplifies to  {y >= x} . Backing over the negative of the  if  condition, we get  {(y >= x) && (x < y)}  which simplifies to  {x < y} . max = y; {(x >= y && max == x) || (x < y && max == y)} if (x >= y) { max = x; } else { max = y; } {(x >= y && max == x) || (x < y && max == y)} Conditional Statements (cont.)
if (x >= y) { max = x; } else { max = y; } {(x >= y && max == x) || (x < y && max == y)} Combining the results of each pass, we get: {(x >= y) || (x < y)} Since this is always true, it means that the code segment produces the postcondition for all values of  x  and  y .  We write the precondition as simply  true . Conditional Statements (cont.)
[object Object],[object Object],[object Object],{ P } while ( G ) {  S } { Q } Logical Pretest Loops
[object Object],int i = 0; int s = 1; while (i < 10) { s = s * 2; i = i + 1; } Logical Pretest Loops (cont.) ,[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object],The Reverse Execution Model
[object Object],[object Object],[object Object],The Reverse Execution Model (cont.)
[object Object],[object Object],[object Object],[object Object],[object Object],The Reverse Execution Model (cont.)
[object Object],[object Object],[object Object],[object Object],[object Object],The Reverse Execution Model (cont.)
[object Object],[object Object],Logical Pretest Loops (cont.)
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],/** ** ** @ensure  result == A * B **/ @require old.B >= 0 result == A * B x == A * B Loop invariant: (x == (A*B)–(m*n)) && (n >= 0) (x == (A*B)–(m*n)) && (n >= 0) (x == (A*B)–(m*B)) && (B >= 0) (x == (A*B)–(A*B)) && (B >= 0) (0 == (A*B)–(A*B)) && (B >= 0) (0 == (old.A * old.B)–(old.A * old.B)) && (B >= 0) (0 == 0) && (old.B >= 0) (old.B >= 0) @require B >= 0 Logical Pretest Loops (cont.)
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],/** ** ** @ensure  result == N * N **/ @require true result == N * N x == N * N Loop invariant: (x == N*N–(N–m)*y–(N–m)*(N–m–1)) && (N >= m) (x == N*N–(N–m)*y–(N–m)*(N–m–1)) && (N >= m) How do we find an appropriate loop invariant? (x == N*N–(N–m)–(N–m)*(N–m–1)) && (N >= m) (0 == N*N–(N–m)–(N–m)*(N–m–1)) && (N >= m) (0 == N*N–N–N*(N–1)) && (N >= 0) (0 == (N*N–N*N) && (N >= 0) ((N < 0) && (-N >= 0)) || (!(N < 0) && (N >= 0)) (N < 0) || (N >= 0) true && (N >= 0) N >= 0 true true Logical Pretest Loops (cont.)

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Testing Fundamentals

  • 1. Learn Software Testing Testing and Verification
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  • 40. 1210554 Egyptian Multiplication 2468 490 4936 4936 245 9872 122 19744 19744 61 631808 631808 1 315904 315904 3 157952 157952 7 78976 78976 15 39488 30 1234 1234 981 Remainder “ Doubled” Multiplier “ Halved” Multiplicand
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  • 65. The truecase : produces the precondition {(x >= y && x == x) || (x < y && x == y)} which simplifies to {(x >= y && true) || false} and further simplifies to {x >= y} . Backing over the if condition, we get {(x >= y) && (x >= y)} which simplifies to {x >= y} . max = x; {(x >= y && max == x) || (x < y && max == y)} if (x >= y) { max = x; } else { max = y; } {(x >= y && max == x) || (x < y && max == y)} Conditional Statements (cont.)
  • 66. The falsecase : produces the precondition {(x >= y && y == x) || (x < y && y == y)} which simplifies to {(y == x) || (x < y && true)} and further simplifies to {y >= x} . Backing over the negative of the if condition, we get {(y >= x) && (x < y)} which simplifies to {x < y} . max = y; {(x >= y && max == x) || (x < y && max == y)} if (x >= y) { max = x; } else { max = y; } {(x >= y && max == x) || (x < y && max == y)} Conditional Statements (cont.)
  • 67. if (x >= y) { max = x; } else { max = y; } {(x >= y && max == x) || (x < y && max == y)} Combining the results of each pass, we get: {(x >= y) || (x < y)} Since this is always true, it means that the code segment produces the postcondition for all values of x and y . We write the precondition as simply true . Conditional Statements (cont.)
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