Exam 2 Review

1
Exam 2 Review
Software Testing and Verification Lecture 26

• Prepared by
• Stephen M. Thebaut, Ph.D.
• University of Florida

2
Coverage

• Lectures 16 through 25 (total of 10)
• Required readings 7-8
• King, et al., Is Proof More Cost-Effective than
  Testing?
• Linger, Cleanroom Software Engineering for
  Zero-Defect Software

3
Coverage (contd)

• Optional problem sets 3 and 4
• Axiomatic verification and predicate transforms
• Function-based verification
• Topics
• Formal Program Specification
• Axiomatic Verification
• Predicate Transforms
• Functional Verification
• Cleanroom Software Engineering

4
Other Resources

• Practice Exams
• Lesson Plans (including Self-Check Quiz
  Questions)

5
Ground Rules and Format

• You will have 90 minutes to complete the exam.
• No notes, books, calculators, or PDAs are
  allowed.
• All answers should be given in the spaces
  provided on the exam only.

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Exam Procedures for EDGE Students

• Proctors should schedule a single exam time
  during normal working hours for all students at
  each site. If this is not possible, exams may be
  scheduled outside normal working hours (e.g., in
  the evening).
• Exams are made available to proctors the same day
  they are administered to on-campus students.
• Proctors should return ORIGINAL exams directly to
  the instructor, preferably via overnight delivery.

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Ground Rules and Format (contd)

• Question format may be short answer, matching,
  true/false, fill-in-the-blank, proofs, etc.
• The point-value of each question will be given.

8
Sample Problems

• (4 pts.) Which of the following best captures the
  precise meaning of "P S Q"? (Circle one of
  the following.)
• P holds before S executes and terminates in state
  Q.
• P holds before S executes and Q will hold if S
  terminates.
• if P holds before executing S, S will terminate
  in state Q.
• if P holds before executing S, Q will hold if S
  terminates.

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Sample Problems (contd)

• (5 pts.) Suppose P while b do s Q for some P,
  Q, b, and s. Suppose, too, that K wp(while b do
  s, Q). Which of the following statements are
  NECESSARILY true?
• P ? K
• K ? P
• K ? b s K
• (K ? b) ? Q
• K while b do s Q

10
Sample Problems (contd)

• (6 pts.) Indicate the truth value of each of the
  following assertions.
• xltn y x1 x y-1 y-1ltn ? xx'
• wp(s1, x17) ? y5 s1 xgt0 ? y5
• x5 s2 y3?xgt0 s2 ygt0

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Sample Problems (contd)

• Consider the assertion biga if bgtbig then big
  b end_if bigMax(a,b)
• (4 pts.) Prove the above using the appropriate
  RULE OF INFERENCE. Give the Rule being used and
  show all steps.
• (4 pts.) Use the WEAKEST PRECON-DITION-BASED
  METHOD to prove that the assertion holds. Show
  all steps.

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Sample Problems (contd)

• (13 pts.) Prove the following assertion (not
  shown) using the Repeat_until Rule of Inference
  derived in problem set 3. Clearly state the rule
  and show all steps.
• (8 pts.) Determine the correctness relationships
  between program P and each of the functions below
  (not shown). Circle "C" for Complete, "S" for
  Sufficient, or "N" for Neither.

13
Sample Problems (contd)

• (7 pts.) Identify H0, H1, H2, and Hi such that
  wp(M, yx-k) H0 V H1 V H2 V...V Hi V... where
• M while tltgtk do
• t t-1
• y y1
• end_while
• Express the wp in CLOSED FORM.

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Sample Problems (contd)

• (9 pts.) For program P and function f below,
  prove f P.
• P repeat
• x x-1
• y yt
• until xn
• f (xgtn -gt x,y n,yt(x-n))
• Clearly identify ALL correctness conditions and
  cases that must be considered.

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Sample Problems (contd)

• (contd)
• The ONLY correctness relationship that may be
  ASSUMED to hold is
• (x,y x-1,yt) x x-1 y yt
• ALL others must be proven using the correctness
  conditions/working correctness questions
  considered in class.

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Sample Problems (contd)

• (7 pts.) For program P below, use the Invariant
  Status Theorem to synthesize a limited invariant
  that COULD be used to prove that the program is
  weakly correct with respect to pre-condition
  true and post-condition yx-k using the while
  loop rule of inference. (Show your work.)

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Sample Problems (contd)

• (contd)
• P y 0
• t x
• while tltgtk do
• t t-1 y y1
• end_while

18
Sample Problems (contd)

• (4 pts.) In "Cleanroom Software Engineering for
  Zero-Defect Software," Linger claims that
  statistical usage testing is "more that 20 times
  more effective" than coverage testing at doing
  something. What is it more effective at doing,
  and why is this so?

19
Sample Problems (contd)

• (6 pts.) The following statements concern the
  paper, "Is Proof More Cost-Effective Than
  Testing," by King, et al. Indicate either "true"
  or "false" as appropriate.
• The paper suggests that while Z-based proofs of
  correctness are clearly useful, they are NOT as
  efficient at finding faults as system validation
  tests.

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Sample Problems (contd)

• (contd)
• UK Defense Standards require a formal
  specification and design, as well as formal
  arguments to link specification to design and
  design to code.
• Consistent with DoD and UK Defense standards, the
  system was implemented using the full Ada
  language.

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Exam 2 Review
Software Testing and Verification Lecture 26

• Prepared by
• Stephen M. Thebaut, Ph.D.
• University of Florida