Software Testing & Verification Assignment 4 Group Activity Worksheet KEY

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Software Testing & Verification Assignment 4 Group Activity Worksheet KEY 1. (6 pts.) Which one of the following is the most appropriate interface specification based on pre- and post-conditions for a program that sets variable ILIK to the Index of the Last Instance of K in the non-empty, unsorted array A[1:N] (where N is an integer constant), or to -1 if K is not an instance of A. a. pre-condition: {N≥1 Λ for every 1≤j<N, ¬(A[j]<A[j+1] V A[j]>A[j+1])} post-condition: {[(1≤ILIK≤N Λ A[ILIK]=K Λ for every ILIK<j≤N, A[j]≠K) V (for every 1≤j≤N, ILIK=-1)] Λ UNCH(A,K)} b. pre-condition: {N≥1} post-condition: {[(1≤ILIK≤N Λ A[ILIK]=K Λ for every ILIK<j≤N, A[j]≠K) V ILIK=-1] Λ UNCH(A,K)} c. pre-condition: {N≥1} post-condition: {[(for every 1≤j≤N, A[j]=K Λ ILIK=N) V (for every 1≤j≤N, A[j]≠K) Λ ILIK=-1] Λ UNCH(A,K)} d. pre-condition: {N≥1} post-condition: {[(ILIK=N Λ A[N]=K) V ILIK=-1] Λ UNCH(A,K)} e. pre-condition: {N≥1} post-condition: {[(1≤ILIK≤N Λ A[ILIK]=K Λ for every 1≤j<ILIK, A[j]≠K) V (for every 1≤j≤N, A[K]≠-1) Λ ILIK=-1] Λ UNCH(A,K)} f. pre-condition: {N≥1} post-condition: {[(1≤ILIK≤N Λ A[ILIK]=K Λ for every ILIK<j≤N, A[j]≠K) V (for every 1≤j≤N, A[j]≠K Λ ILIK=-1)] Λ UNCH(A,K)} g. pre-condition: {N≥1} post-condition: {[(1≤ILIK≤N Λ A[ILIK]=K Λ for every 1≤j<ILIK, A[j]≠K) V (for every 1≤j≤N, A[j]≠K) Λ ILIK=-1] Λ UNCH(A,K)}

2. (4 pts.) Which one of the following most accurately reflects the meaning of the weak correctness predicate, "{P} S {Q}"? (Circle ONE only.) a. ( {P} S {Q} ) ≡ “P must hold before S executes and Q must hold when S terminates” b. “Q could be false when S terminates” ≡ ¬( {P} S {Q} ) c. If P holds before executing S, S must terminate in state Q. d. {P} S {Q} ≡ [(“P is false before S executes”) V (“S does not terminate”) V “Q must be true when S terminates given that P is true before S executes”) e. {P} S {Q} is true unless Q is always false when S terminates, given that P is true before S executes. f. (none of the above)

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2 3. (10 pts.) Consider the assertion of weak correctness: {x>0} S {y=z+x}. Which of the following facts would logically imply that this assertion is FALSE and which would not? Circle either “would” or “would not” as appropriate. Consider each fact given independently. To compensate for random guessing, you will receive +2 pts. for each correct answer and -2 pts. for each incorrect answer. a. When the initial value of x is -5, S terminates with y=z+x.

would

would not

b. When the initial value of x is 5, S terminates with y=z.

would

would not

c. For all initial values of x<10, S terminates with the final value of y being less than z+x.

would

would not

d. For at least one initial value of x satisfying the given pre-condition, S terminates with y=z-x.

would

would not

e. Whenever the initial value of x is greater than -5, S does not terminate.

would

would not

4. (20 pts.) Circle either “true” or “false” for each of the following assertions. Note that to compensate for random guessing, you will receive +2 pts. for each correct answer and -2 pts. for each incorrect answer. a. [{x=17} S {x=17}]  [{x>0} S {x>0}]

true

false

b. [{x>0} S {x=17}]  [{x=17} S {x>0}]

true

false

c. {z=x(y-n)} y := y+1 {z-x=x(y-n)}

true

false

{z=x(y-n)} y := y+1 {z=x((y-1)-n)} = {z=xy-x-xn)} = {z+x=xy-xn)} = {z+x=x(y-n)} which is NOT, in general, equal to the given post-condition {z-x=x(y-n)} d. {z=x(y-n)} n := n+1 {z=x(y-n+1)}

true

false

{z=x(y-n)} n := n+1 {z=x(y-(n-1))} = {z=x(y-n+1))} which IS the given post-condition. e. [P  (¬b Л Q)]  [{P} if b then S {Q}]

true

false

f. {P} S1;S2 {Q}  [{P} S1 {true} Л {true} S2 {Q}]

true

false

g. {P} while b do S {Q}

true

false

h. {x=t Л y=1} y := y+1; x := x-1; a := 4 {y=t-x Л a=4}

true

false

i. {x[i]=j} i := i+1 {x[i+1]=j}

true

false



{P} if b then S end_if; if b then S end_if; while b do S end_while {Q}

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3 j. ([{P Л b} S {Q}] V [(P Л ¬b)  Q])  {P} if b then S {Q}

true

false

5. (6 pts.) Consider the hypothesized invariant for the while-do statement in the following assertion: Which one of the following correctly identifies the while_do statement ROI antecedent(s) that hold for this loop and the given hypothesized invariant? (Circle ONE only.) a. initialization only (2 pts.)

e. initialization and finalization only (6 pts.)

b. preservation only (0 pts.)

f. initialization and preservation only (0 pts.)

c. finalization only (2 pts.)

g. initialization, preservation, and finalization (4 pts.)

d. preservation and finalization only (0 pts.)

h. none of the antecedents would hold (2 pts.)

Note: as explained in class, the set of index values from i=1 to i=0 is empty, so the sum of array X from i=1 to i=0 is 0.

6. (9 pts.) Circle either “valid” or “invalid” for each of the following hypothesized Rules of Inference. To compensate for random guessing, you will receive +3 pts. for each correct answer and -3 pts. for each incorrect answer.

Q => (~b) a. --------------------------------------------------------------------- ? {P} while b do S {Q}

valid

invalid

(P Л ~b) => Q, {P Л b} s {I}, {I Л b} s {I}, (I Л ~b) => Q b. --------------------------------------------------------------------------------------- ? {P} while b do s {Q}

valid

invalid

{true} S {I}, (I Л b)  Q c. ---------------------------------------------------------------------- ? {P} repeat S until b {Q}

valid

invalid

7. (5 pts.) Consider the INVALID hypothesized ROI: {true} S {I} strongly, (I Λ b)  Q -------------------------------------------------------- ? {P} repeat S until b {Q} strongly This study source was downloaded by 100000858468549 from CourseHero.com on 04-02-2023 01:23:00 GMT -05:00

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4 The ROI is INVALID. Which one of the following constitutes a counterexample that proves this? (Circle ONE only.) i. {true} repeat x := -5 until x=-5 {x=-5} with I: true

consequent true

ii. {true} repeat x := -5 until x=-5 {x=-5 Λ y=17} with I: true 2nd antecedent false iii. {x=-5} repeat x := x-1 until x=0 {x=0} with I: true iv. {true} repeat x := -5 until x=-5 {x=-5 Λ y=17} with I: y=17 1st antecedent false v. (none of the above) 8. (6 pts.) Circle either “true” or “false” for each of the following assertions. To compensate for random guessing, you will receive +2 pts. for each correct answer and -2 pts. for each incorrect answer. a. Z=XJ is a loop invariant for the assertion:

true

false

b. Z=XJ Л J≤Y is a Q-adequate loop invariant for the assertion given in part (a) above.

true

false

c. {P} repeat S until b {Q}

true

false

{Z=0 Л J=0} while J<Y do Z := Z+X; J := J+1 end_while {Z=XY}



{P} S; while NOT b do S end_while {Q}

9. (6 pts.) Consider the hypothesized invariant I: y=t-x Л a=4 for the following assertion: {x=t Л y=0} repeat y := y+1; x := x-1; a := 4 until x=0 {y=t Л a=4} Which one of the following correctly identifies the repeat_until statement ROI antecedent(s) that hold for this loop and the given hypothesized invariant? (Circle ONE only.) a. initialization only (2 pts.)

e. initialization and finalization only (4 pts.)

b. preservation only (2 pts.)

f. initialization and preservation only (4 pts.)

c. finalization only (2 pts.)

g. initialization, preservation, and finalization (6 pts.)

d. preservation and finalization only (4 pts.)

h. none of the antecedents would hold (0 pts.)

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