[klee-dev] Option for generating MC/DC testcases

[Damir]

Hello everyone!

I've recently started using KLEE, and I'm wondering how hard it would be to
implement full MC/DC testcases generation in KLEE.

You can read about MC/DC on Wiki

https://en.wikipedia.org/wiki/Modified_condition/decision_coverage

I've done some analysis, and figured out how it can be done in klee,
theoretically,

As I see it, implementing such feature would require tampering with forking
mechanism in KLEE, in following ways:

1) Allow breaking a complex decision into conditions, for example

    if (A && B && C)
the decision is (A && B && C) here, and conditions are A, B and C.

 All conditions are functions of symbolic variables, returning boolean, and
combined into decision using only boolean logic.

2) Instead of forking on whether decision is true or false, forks are based
on conditions.

Before (current KLEE):

fork 1: Decision(A, B, C) == false
fork 2: Decision(A, B, C) == true

MC/DC way:

Before forking, set of conditions (in addition to previous ones) must be
solved:

For example, for condition A:

A(x1, y1, ... z1) == false
A(x2, y2, ... z2) == true

B(x1, y1, ... z1) == Bfixed
B(x2, y2, .... z2) == Bfixed

C(x1, y1, ... z1) == Cfixed
C(x2, y2, .... z2) == Cfixed

Decision(x1, y1, ... z1) != Decision(x2, y2, ... z2)

If there is a solution (Bfixed, Cfixed) to those constraints, two forks are
created with following conditions on them:

fork 1: A == true, B == Bfixed, C == Cfixed
fork 2: A == false, B == Bfixed, C == Cfixed

If there is no solution to those constraints, then the decision cannot be
covered by MC/DC criteria, this can be reported, and forking on this
condition can be done in a simple way (condition coverage):

fork1:  A == true
fork2:  A == false
and then the usual way, fork on (Decision(A,B,C) == false and Decision(A,
B, C) == true)

So, basically during MC/DC, maximum number of forks is 4 * number of
conditions.

3) Testcases can be optimized by removing duplicates.

Example 1:

if x is a symbolic variable, and decision is (x > 0 && x < 10), here how it
can be handled in MC/DC way:

1) Determine that there are two separate conditions, A(x) = (x > 0) and
B(x) = (x < 10).
2) For condition A, following set of constraints is introduced:
   A(x1) == false
   A(x2) == true
   B(x1) == Bfixed
   B(x2) == Bfixed
   A(x1) && B(x1) != A(x2) && B(x2)

 It is solved, and is found that Bfixed is true.
 So, fork is created with following conditions:

  Fork1:  (x > 0) == true , (x < 10) == true, satisfied, testcase is x == 1
  Fork2:  (x > 0) == false , (x < 10) == true, satisfied, testcase is x == 0

For condition B, the same procedure applies.
set of constaints is following:
    A(x1) == Afixed
    A(x2) == Afixed
    B(x1) == false
    B(x2) == true
    A(x1) && B(x1) != A(x2) && B(x2)

  It is solved, and is found that Afixed is true.

   Fork is created with following conditions:
   Fork3: x > 0) == true,  (x < 10) == true, satisfied, testcase is x == 1
   Fork4: x > 0) == true,  (x < 10) == false, satisfied, testcase is x == 10

since condition for fork3 is the same as for fork1, it will produce the
same testcases, and duplicates can be discarded.

So, three testcases are generated, x == 0, x == 1 and x == 10. When
combined, they satisfy MC/DC criteria on given decision.

Example 2:
The same as Example 1, but decision is now (x > 0 && x > 10)

1) There are two separate conditions, A(x) = (x > 0) and B(x) = (x > 10)
2) Constraints set for condition A is
  A(x1) == false
  A(x2) == true
  B(x1) == Bfixed
  B(x2) == Bfixed
  A(x1) && B(x1) != A(x2) && B(x2)

This set of restraints is unsatisfiable, so MC/DC cannot be reached on
condtion A. Most probably, condition A is redundant.
Then, forking is created using condition coverage:

Fork1: (x > 0) == true
Fork2: (x > 0) == false

Then additional forks are created as usual,
Fork 11: (x > 0) == true, (x > 0 && x > 10) == true - satisfied, testcase
is x = 11
Fork 12: (x > 0) == true, (x > 0 && x > 10) == false - satisfied, testcase
is x == 1

Fork 21: (x > 0) == false, (x > 0 && x > 10) == true - unsatisfied
Fork 22: (x > 0) == false, (x > 0 && x > 10) == false, satisfied, testcase
is x = 0

For condition B, constraint is:
  A(x1) == Afixed
  A(x2) == Afixed
  B(x1) == false
  B(x2) == true
  A(x1) && B(x1) != A(x2) && B(x2)

  When solved, it gives Afixed = true.

  Fork3: (x > 0) == true, (x > 10) == true, satisfied, testcase is x == 11
  Fork4: (x > 0) == true, (x > 10) == false, satisfied, testcase is x == 1

After removing duplicate testcases, three testcases remain:  x == 0,. x ==
1 and x == 11. They do not satisfy MC/DC criteria though, and warning can
be produced,
that condition A cannot be covered by MC/DC on every path.

Thanks for reading up to this point!

The question is, any idea, how this procedure can be implemented in KLEE? I
see it as an option to klee, turning it on would enable MC/DC analysis,
generate more testcases
and produce warnings if some decisions cannot satisfy MC/DC criteria.

Where can I start, what files I should change to implement it?

---
With best regards,
Damir Shaykhutdinov (lost404 at gmail.com)
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