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Delta Debugging

Delta Debugging. Lecture 2 CS 6340. How do we go from this .

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Delta Debugging

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  1. Delta Debugging Lecture 2CS 6340

  2. How do we go from this ... <td align=left valign=top><SELECT NAME="op sys" MULTIPLE SIZE=7><OPTION VALUE="All">All<OPTION VALUE="Windows 3.1">Windows 3.1<OPTION VALUE="Windows 95">Windows 95<OPTION VALUE="Windows 98">Windows 98<OPTION VALUE="Windows ME">Windows ME<OPTION VALUE="Windows 2000">Windows 2000<OPTION VALUE="Windows NT">Windows NT<OPTION VALUE="Mac System 7">Mac System 7<OPTION VALUE="Mac System 7.5">Mac System 7.5<OPTION VALUE="Mac System 7.6.1">Mac System 7.6.1<OPTION VALUE="Mac System 8.0">Mac System 8.0<OPTION VALUE="Mac System 8.5">Mac System 8.5<OPTION VALUE="Mac System 8.6">Mac System 8.6<OPTION VALUE="Mac System 9.x">Mac System 9.x<OPTION VALUE="MacOS X">MacOS X<OPTION VALUE="Linux">Linux<OPTION VALUE="BSDI">BSDI<OPTION VALUE="FreeBSD">FreeBSD<OPTION VALUE="NetBSD">NetBSD<OPTION VALUE="OpenBSD">OpenBSD<OPTION VALUE="AIX">AIX<OPTION VALUE="BeOS">BeOS<OPTION VALUE="HP-UX">HP-UX<OPTION VALUE="IRIX">IRIX<OPTION VALUE="Neutrino">Neutrino<OPTION VALUE="OpenVMS">OpenVMS<OPTION VALUE="OS/2">OS/2<OPTION VALUE="OSF/1">OSF/1<OPTION VALUE="Solaris">Solaris<OPTION VALUE="SunOS">SunOS<OPTION VALUE="other">other</SELECT></td><td align=left valign=top><SELECT NAME="priority" MULTIPLE SIZE=7> <OPTION VALUE="--">--<OPTION VALUE="P1">P1<OPTION VALUE="P2">P2<OPTION VALUE="P3">P3<OPTION VALUE="P4">P4<OPTION VALUE="P5">P5</SELECT></td><td align=left valign=top><SELECT NAME="bug severity" MULTIPLE SIZE=7><OPTION VALUE="blocker">blocker<OPTION VALUE="critical">critical<OPTION VALUE="major">major<OPTION VALUE="normal">normal<OPTION VALUE="minor">minor<OPTION VALUE="trivial">trivial<OPTION VALUE="enhancement">enhancement</SELECT></tr></table> File Print Segmentation Fault

  3. ... to this? <SELECT> File Print Segmentation Fault

  4. Simplification Once one has reproduced a problem, one must find out what’s relevant • Does failure really depend on 10,000 lines of input? • Does failure really require this exact schedule? • Does failure really need this sequence of calls?

  5. Why Simplify? • Ease of communication: a simplified test case is easier to communicate • Easier debugging: smaller test cases result in smaller states and shorter executions • Identify duplicates: simplified test cases subsume several duplicates

  6. Real-World Scenario • The Mozilla open-source web browser project receives several dozens bug reports a day • Each bug report has to be simplified • Eliminate all details irrelevant to producing the failure • To facilitate debugging • To make sure it does not replicate a similar bug report • In July 1999, Bugzilla listed more than 370 open bug reports for Mozilla • These were not even simplified • Mozilla engineers were overwhelmed with work • They created the Mozilla BugAThon: a call for volunteers to process bug reports

  7. Real-World Scenario • The Mozilla open-source web browser project receives several dozens bug reports a day • Each bug report has to be simplified • Eliminate all details irrelevant to producing the failure • To facilitate debugging • To make sure it does not replicate a similar bug report • In July 1999, Bugzilla listed more than 370 open bug reports for Mozilla • These were not even simplified • Mozilla engineers were overwhelmed with work • They created the Mozilla BugAThon: a call for volunteers to process bug reports Today: For 15 bug reports simplified, you get a Firefox plushie https://developer.mozilla.org/en/Gecko_BugAThon • For 5 bug reports simplified, the volunteer would be invited to the launch party; 20 bugs would earn a T-shirt signed by the grateful engineers.

  8. Your Solution • How do you solve these problems? • Binary search • Cut the test case in half • Iterate • Brilliant idea: Why not automate this?

  9. Binary Search • Proceed by binary search. Throw away half the input and see if the output is still wrong. • If not, go back to the previous state and discard the other half of the input.

  10. Binary Search • Proceed by binary search. Throw away half the input and see if the output is still wrong. • If not, go back to the previous state and discard the other half of the input. ✘

  11. Binary Search • Proceed by binary search. Throw away half the input and see if the output is still wrong. • If not, go back to the previous state and discard the other half of the input.

  12. Binary Search • Proceed by binary search. Throw away half the input and see if the output is still wrong. • If not, go back to the previous state and discard the other half of the input. ✘

  13. Binary Search • Proceed by binary search. Throw away half the input and see if the output is still wrong. • If not, go back to the previous state and discard the other half of the input.

  14. Binary Search • Proceed by binary search. Throw away half the input and see if the output is still wrong. • If not, go back to the previous state and discard the other half of the input. ✘

  15. Binary Search • Proceed by binary search. Throw away half the input and see if the output is still wrong. • If not, go back to the previous state and discard the other half of the input.

  16. Binary Search • Proceed by binary search. Throw away half the input and see if the output is still wrong. • If not, go back to the previous state and discard the other half of the input. ✔

  17. Binary Search • Proceed by binary search. Throw away half the input and see if the output is still wrong. • If not, go back to the previous state and discard the other half of the input.

  18. Binary Search • Proceed by binary search. Throw away half the input and see if the output is still wrong. • If not, go back to the previous state and discard the other half of the input. ✘

  19. Binary Search • Proceed by binary search. Throw away half the input and see if the output is still wrong. • If not, go back to the previous state and discard the other half of the input. ✔

  20. Binary Search • Proceed by binary search. Throw away half the input and see if the output is still wrong. • If not, go back to the previous state and discard the other half of the input. ✔

  21. Binary Search • Proceed by binary search. Throw away half the input and see if the output is still wrong. • If not, go back to the previous state and discard the other half of the input. Simplified input

  22. Complex Input <td align=left valign=top><SELECT NAME="op sys" MULTIPLE SIZE=7><OPTION VALUE="All">All<OPTION VALUE="Windows 3.1">Windows 3.1<OPTION VALUE="Windows 95">Windows 95<OPTION VALUE="Windows 98">Windows 98<OPTION VALUE="Windows ME">Windows ME<OPTION VALUE="Windows 2000">Windows 2000<OPTION VALUE="Windows NT">Windows NT<OPTION VALUE="Mac System 7">Mac System 7<OPTION VALUE="Mac System 7.5">Mac System 7.5<OPTION VALUE="Mac System 7.6.1">Mac System 7.6.1<OPTION VALUE="Mac System 8.0">Mac System 8.0<OPTION VALUE="Mac System 8.5">Mac System 8.5<OPTION VALUE="Mac System 8.6">Mac System 8.6<OPTION VALUE="Mac System 9.x">Mac System 9.x<OPTION VALUE="MacOS X">MacOS X<OPTION VALUE="Linux">Linux<OPTION VALUE="BSDI">BSDI<OPTION VALUE="FreeBSD">FreeBSD<OPTION VALUE="NetBSD">NetBSD<OPTION VALUE="OpenBSD">OpenBSD<OPTION VALUE="AIX">AIX<OPTION VALUE="BeOS">BeOS<OPTION VALUE="HP-UX">HP-UX<OPTION VALUE="IRIX">IRIX<OPTION VALUE="Neutrino">Neutrino<OPTION VALUE="OpenVMS">OpenVMS<OPTION VALUE="OS/2">OS/2<OPTION VALUE="OSF/1">OSF/1<OPTION VALUE="Solaris">Solaris<OPTION VALUE="SunOS">SunOS<OPTION VALUE="other">other</SELECT></td><td align=left valign=top><SELECT NAME="priority" MULTIPLE SIZE=7> <OPTION VALUE="--">--<OPTION VALUE="P1">P1<OPTION VALUE="P2">P2<OPTION VALUE="P3">P3<OPTION VALUE="P4">P4<OPTION VALUE="P5">P5</SELECT></td><td align=left valign=top><SELECT NAME="bug severity" MULTIPLE SIZE=7><OPTION VALUE="blocker">blocker<OPTION VALUE="critical">critical<OPTION VALUE="major">major<OPTION VALUE="normal">normal<OPTION VALUE="minor">minor<OPTION VALUE="trivial">trivial<OPTION VALUE="enhancement">enhancement</SELECT></tr></table> File Print Segmentation Fault

  23. Simplified Input • <SELECT NAME="priority" MULTIPLE SIZE=7> • Simplified from 896 lines to one single line • Required only 12 tests

  24. Binary Search • <SELECT NAME="priority" MULTIPLE SIZE=7>

  25. Binary Search ✘ • <SELECT NAME="priority" MULTIPLE SIZE=7>

  26. Binary Search ✘ • <SELECT NAME="priority" MULTIPLE SIZE=7> • <SELECT NAME="priority" MULTIPLE SIZE=7> ✔

  27. Binary Search ✘ • <SELECT NAME="priority" MULTIPLE SIZE=7> • <SELECT NAME="priority" MULTIPLE SIZE=7> • <SELECT NAME="priority" MULTIPLE SIZE=7> ✔ ✔

  28. Binary Search ✘ • <SELECT NAME="priority" MULTIPLE SIZE=7> • <SELECT NAME="priority" MULTIPLE SIZE=7> • <SELECT NAME="priority" MULTIPLE SIZE=7> What do we do if both halves pass? ✔ ✔

  29. Change Granularity

  30. Change Granularity

  31. General Delta-Debugging Algorithm Basic idea: • Start with few & large changes first • If all alternatives pass or are unresolved, apply more & smaller changes. ∆1 ∆2 ∆1 ∆2 ∆1 ∆2 ∆3 ∆4 ∆5 ∆6 ∆7 ∆8 ∆1 ∆2 ∆3 ∆4 ∆5 ∆6 ∆7 ∆8

  32. Binary Search ✘ • <SELECT NAME="priority" MULTIPLE SIZE=7> • <SELECT NAME="priority" MULTIPLE SIZE=7> • <SELECT NAME="priority" MULTIPLE SIZE=7> ✔ ✔

  33. Binary Search ✘ • <SELECT NAME="priority" MULTIPLE SIZE=7> • <SELECT NAME="priority" MULTIPLE SIZE=7> • <SELECT NAME="priority" MULTIPLE SIZE=7> • <SELECT NAME="priority" MULTIPLE SIZE=7> ✔ ✔ ✔

  34. Binary Search ✘ • <SELECT NAME="priority" MULTIPLE SIZE=7> • <SELECT NAME="priority" MULTIPLE SIZE=7> • <SELECT NAME="priority" MULTIPLE SIZE=7> • <SELECT NAME="priority" MULTIPLE SIZE=7> • <SELECT NAME="priority" MULTIPLE SIZE=7> ✔ ✔ ✔ ✘

  35. Binary Search ✘ • <SELECT NAME="priority" MULTIPLE SIZE=7> • <SELECT NAME="priority" MULTIPLE SIZE=7> • <SELECT NAME="priority" MULTIPLE SIZE=7> • <SELECT NAME="priority" MULTIPLE SIZE=7> • <SELECT NAME="priority" MULTIPLE SIZE=7> • <SELECT NAME="priority" MULTIPLE SIZE=7> ✔ ✔ ✔ ✘ ✘

  36. Binary Search ✘ • <SELECT NAME="priority" MULTIPLE SIZE=7> • <SELECT NAME="priority" MULTIPLE SIZE=7> • <SELECT NAME="priority" MULTIPLE SIZE=7> • <SELECT NAME="priority" MULTIPLE SIZE=7> • <SELECT NAME="priority" MULTIPLE SIZE=7> • <SELECT NAME="priority" MULTIPLE SIZE=7> • <SELECT NAME="priority" MULTIPLE SIZE=7> ✔ ✔ ✔ ✘ ✘ ✔

  37. Inputs and Failures • Let E be the set of possible inputs • rP E corresponds to an input that passes • rF E corresponds to an input that fails

  38. Binary Search ✘ • <SELECT NAME="priority" MULTIPLE SIZE=7> • <SELECT NAME="priority" MULTIPLE SIZE=7> • <SELECT NAME="priority" MULTIPLE SIZE=7> • <SELECT NAME="priority" MULTIPLE SIZE=7> • <SELECT NAME="priority" MULTIPLE SIZE=7> • <SELECT NAME="priority" MULTIPLE SIZE=7> • <SELECT NAME="priority" MULTIPLE SIZE=7> Example of rFand rP? ✔ ✔ ✔ ✘ ✘ ✔

  39. Binary Search ✘ • <SELECT NAME="priority" MULTIPLE SIZE=7> • <SELECT NAME="priority" MULTIPLE SIZE=7> • <SELECT NAME="priority" MULTIPLE SIZE=7> • <SELECT NAME="priority" MULTIPLE SIZE=7> • <SELECT NAME="priority" MULTIPLE SIZE=7> • <SELECT NAME="priority" MULTIPLE SIZE=7> • <SELECT NAME="priority" MULTIPLE SIZE=7> Example of rFand rP? rF= <SELECT NALE SIZE=7> rP= <SELECT NAME="priori ✔ ✔ ✔ ✘ ✘ ✔

  40. Changes • We can go from one input to another by changes • A change  is a mapping  : E  E which takes one input and changes it to another input • Example: ’ = insert ME="priori at appropriate position r1 = <SELECT NAty" MULTIPLE SIZE=7> What is ’(r1)? <SELECT NAME="priority" MULTIPLE SIZE=7>

  41. Decomposing Changes • A change  can be decomposed to a number of elementary changes 1, 2, ..., n where= 1 o 2 o ... o n and (i o j)(r) = i(j(r)) • For example, deleting a part of the input file can be decomposed to deleting characters one be one from the file • in other words: by composing deleting of single characters,we can get a change that deletes part of the input file ’ = insert ME="priori ’ = 1 o 2 o 3 o 4 o 5 o 6 o 7 o 8 o 9 o 10 • 1 = insert M • 2 = insert E • …

  42. Summary • We have an input without failure: rP • We have an input with failure: rF • We have a set of changes cF = {1, 2, ..., n } such that: rF= (1 o 2 o ... o n )(rP) • Each subset c of cF is a test case

  43. Testing Test Cases • Given a test case c, we would like to know if input generated by applying changes in c to rPcauses a failure • We define the following function: test: Powerset(cF)  {P, F, ?} such that, given c = {1, 2, ..., m} cF test(c) = F iff (1 o 2 o ... o m )(rP) is a failing input

  44. Minimizing Test Cases • Now the question is: Can we find the minimal test case c such that test(c) = F? • A test case c  cF is called the global minimum of cFif: for all c’ cF , |c’| < |c|  test(c’)  F • Global minimum is the smallest set of changes which will make the program fail • Finding the global minimum may require us to perform exponential number of tests

  45. Search for 1-minimal Input • Different problem formulation: Find a set of changes that cause the failure, but removing any change causes the failure to go away • This is 1-minimality

  46. Minimizing Test Cases • A test case c  cF is called a local minimum of cFif: for all c’ c. test(c’)  F • A test case c  cF is n-minimal if: for all c’ c. |c|  |c’|  n  test(c’)  F • A test case is 1-minimal if: for all i  c. test(c – {i})  F

  47. Naïve Algorithm • To find a 1-minimal subset of c: • If for all i  c. test(c – {i})  F, then c is 1-minimal • Else recurse on c – {} for some   c. test(c – {}) = F

  48. Analysis • In the worst case, • We remove one element from the set per iteration • After trying every other element • Work is potentially N + (N-1) + (N-2) + … • This is O(N2)

  49. Work Smarter, Not Harder • We can often do better • Silly to start out removing 1 element at a time • Try dividing change set in 2 initially • Increase # of subsets if we can’t make progress • If we get lucky, search will converge quickly

  50. Minimization Algorithm • The delta debugging algorithm finds a 1-minimal test case • It partitions the set cF to 1, 2, ... n • 1, 2, ... nare pairwise disjoint • cF = 1  2  ...  n • Define the complement of i as i = cF i • Start with n = 2 • Tests each test case defined by partition and their complements • Reduce test case if a smaller failure inducing set is found • otherwise refine the partition, i.e. n = n*2

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