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Efficient State Model Checking for Programs: Enhancing Software Quality

This thesis focuses on improving model checking for software testing, particularly for programs with dynamically allocated data. It explores ways to speed up state-space exploration, enhancing software quality and testing efficiency. The study aims to streamline operations like transition execution, path exploration, and path pruning for effective model checking. Traditional and modern model checkers are examined, with a goal to automate testing and identify errors efficiently. The research delves into exploring interesting behaviors, systematic testing, and behavior modeling to advance software quality assurance.

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Efficient State Model Checking for Programs: Enhancing Software Quality

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  1. EFFICIENT EXPLICIT-STATE MODEL CHECKING FOR PROGRAMS WITH DYNAMICALLY ALLOCATED DATA Marcelo d’Amorim Ph.D. thesis committee: Gul Agha Jennifer Hou Darko Marinov (advisor, chair) Mahesh Viswanathan August 06, 2007

  2. Testing is important • Programmers develop software with lots of errors • Testing is the dominant approach in industry to assure software quality • But...testing is expensive [NIS02] test automation can assist the programmer in finding errors

  3. model checkers are tools that can assist in the automation of software testing goal: improve model checking for software testing

  4. Reminder about Prelim exam • Work presented at Prelim • Symclat (ASE’06 paper) • Improved software testing without model checking • Mixed Execution (ICFEM’06 paper) • More efficient model checking • Delta Execution Idea • More efficient model checking • Work done since Prelim • Delta Execution (ISSTA’07 paper) focus of my thesis

  5. Model Checking and Testing • Model describes behaviors of a system • description includes states and transition • The model checker performs state-space exploration on the input model • … performs systematic testing model “interesting” behaviors model checker property

  6. Design and implementation models • Traditionally, model checkers operate on design models • FDR [Ros94], SPIN [Hol97], NuSMV [CCGR99], Alloy Analyzer [Jac00]… • Recently, more common for model checkers to operate on programs • JPF [JV01], CMC [MPC+02], Bogor [RDH03], SpecExplorer [VCST05]…

  7. Design and implementation models • Traditionally, model checkers operate on design models • FDR [Ros94], SPIN [Hol97], NuSMV [CCGR99], Alloy Analyzer [Jac00]… • Recently, more common for model checkers to operate on programs • JPF [JV01], CMC [MPC+02], Bogor [RDH03], SpecExplorer [VCST05]… focus

  8. Goal speed up state-space exploration for programs with dynamically allocated data (/OO programs)

  9. Example: test subject • BinarySearchTree (BST) and Node classes: state public class BinarySearchTree { private Node root; private int size; public void add(int info) {…} public boolean remove(int info) {…} } class Node { Node left, right; int info; Node(int info) { this.info = info } } 1 2 2 operations

  10. Example: test sequence • Examples of sequences sequences of method calls from the initial state BinarySearchTree bst = new BinarySearchTree(); bst.add(1); bst.add(2); BinarySearchTree bst = new BinarySearchTree(); bst.add(2); bst.remove(1);

  11. Example scenario: Bounded-Exhaustive Exploration • Examples of sequences explore all sequences up to given bounds: • length of sequence • range of values BinarySearchTree bst = new BinarySearchTree(); bst.add(1); bst.add(2); BinarySearchTree bst = new BinarySearchTree(); bst.add(2); bst.remove(1);

  12. Example scenario: Bounded-Exhaustive Exploration bounds // L: length of sequence // N: number of input values // in most experiments L == N public static void main(int L, int N) { BST bst = new BST(); // empty tree for (int i = 0; i < L; i++) { int methNum = Verify.getInt(0, 1); int value = Verify.getInt(1, N); switch (methNum) { case 0: bst.add(value); break; case 1: bst.remove(value); break; } stopIfVisited(bst); } }

  13. Example: Bounded-Exhaustive Exploration L = N = 2 0  remove(2) add(1) add(2) remove(1) • chooses method and value

  14. Example: Bounded-Exhaustive Exploration L = N = 2 0  remove(2) add(1) add(2) remove(1) 1 1 • chooses method and value • executes transition

  15. Example: Bounded-Exhaustive Exploration L = N = 2 0  remove(2) add(2) add(1) remove(1) 1 1 • chooses method and value • executes transition • explores paths (backtracking)

  16. Example: Bounded-Exhaustive Exploration L = N = 2 0  remove(2) add(2) add(1) remove(1) 2 1 1 1 • chooses method and value • executes transition • explores paths (backtracking)

  17. Example: Bounded-Exhaustive Exploration L = N = 2 0  remove(2) add(2) add(1) remove(1) 0 2 1 1 1 • chooses method and value • executes transition • explores paths (backtracking) • prunes paths (compares state)

  18. Example: Bounded-Exhaustive Exploration L = N = 2 0  remove(2) add(2) add(1) remove(1) 0 0 2 1 1 1 • chooses method and value • executes transition • explores paths (backtracking) • prunes paths (compares state)

  19. Example: Bounded-Exhaustive Exploration L = N = 2 0  remove(2) add(2) add(1) remove(1) 0 0 2 1 1 1  … add(1) • chooses method and value • executes transition • explores paths (backtracking) • prunes paths (compares state) 1 1

  20. Example: Bounded-Exhaustive Exploration L = N = 2 0  remove(2) add(2) add(1) remove(1) 0 0 2 1 1 1  … add(1) • chooses method and value • executes transition • explores paths (backtracking) • prunes paths (compares state) add(2) 1 1 2 1 2

  21. Operations • Costly operations for an important class of model checkers: • execution of transitions • exploration of paths (backtracking) • pruning of paths (state comparison) specific goal is to speed up these operations

  22. Our contributions • Two techniques • Mixed execution • Delta execution (∆Execution) • Overall time reduction • execution (mixed and ∆) • backtracking (∆) • state comparison (∆)

  23. Outline • Introduction & Goal • ∆Execution • Mixed execution (brief) • Related Work and Conclusions

  24. Our Technique: ∆Execution • Observation: • Many of the execution paths in state-space exploration partially overlap • Different states can hold same values ∆Execution exploits these overlaps across executions and states to speed up model checking

  25. Example • Consider separately invoking the method call add(4) on the following two Binary Search Trees BST #1 BST #2 3 3 2 1 1 3 3 2

  26. Example 3 2 1 3 1: public void add(int elem) 2: if (root == null) 3: root = new Node(elem) 4: else 5: for (Node temp = root; true; ) 6: if (temp.info < elem) 7: if (temp.right == null) { 8: temp.right = new Node(elem) 9: break; 10: } else temp = temp.right; 11: } else if (temp.info > elem) { 12: if (temp.left = null) { 13: temp.left = new Node(elem); 14: break; 15: } else temp = temp.left; 16: } else return; // no duplicates 17: size++; 18: }

  27. Example 3 2 1 3 4 2 1 3 4 Execution Trace: 1 , 2 , 4 , 5 , 6 , 7 , 10 5 , 6 , 7 , 8 , 9 , 17 1: public void add(int elem) 2: if (root == null) 3: root = new Node(elem) 4: else 5: for (Node temp = root; true; ) 6: if (temp.info < elem) 7: if (temp.right == null) { 8: temp.right = new Node(elem) 9: break; 10: } else temp = temp.right; 11: } else if (temp.info > elem) { 12: if (temp.left = null) { 13: temp.left = new Node(elem); 14: break; 15: } else temp = temp.left; 16: } else return; // no duplicates 17: size++; 18: }

  28. Example 3 2 1 3 4 2 1 3 4 Execution Trace: 1 , 2 , 4 , 5 , 6 , 7 , 10 5 , 6 , 7 , 8 , 9 , 17 3 1: public void add(int elem) 2: if (root == null) 3: root = new Node(elem) 4: else 5: for (Node temp = root; true; ) 6: if (temp.info < elem) 7: if (temp.right == null) { 8: temp.right = new Node(elem) 9: break; 10: } else temp = temp.right; 11: } else if (temp.info > elem) { 12: if (temp.left = null) { 13: temp.left = new Node(elem); 14: break; 15: } else temp = temp.left; 16: } else return; // no duplicates 17: size++; 18: } 1 3 2 4 1 3 2 4

  29. Example Execution overlap across states 4 4 1 2 overlap across executions 3 1 3 2 4 4 Execution Trace: 1 , 2 , 4 , 5 , 6 , 7 , 10 5 , 6 , 7 , 8 , 9 , 17

  30. ∆Execution • Technique: uses “set of states” to perform state-space exploration • Exploits the overlapping on states and executions • Reduce time: • execution of transitions • exploration of paths (backtracking) • pruning of paths (state comparison)

  31. 0 1 1 1 1 1 1 2 0 1 2 2 2 2 2 1 1 1 1 2 0 standard exploration  0   0

  32. 0 1 1 1 1 1 1 0  2 0 1 2 2 2 2 2 1 1 1 1 2 2 0 0 1 1 1 2 1 1 1  1 2 1 0 2 1 1 0 2 2 2 1 2 1 1 1 2 1 2 2 1 2 0 standard exploration  0   0 delta exploration

  33. Back to our example 3 1 3 2 3 2 1 3 only one execution add(4) only one update on field size 4 4 2 1 1 3 3 2 4 4

  34. ∆Execution: Set Operations • Merge: “merges” sets of states into one ∆State • Split: “splits” a set of states into two subsets

  35. Combined Execution & Splitting 3 3 3 3 3 3 3 2 1 1 2 1 1 3 3 2 1 2 2 3 add(4)

  36. Combined Execution & Splitting 3 3 3 3 3 3 3 2 1 1 2 1 1 3 3 2 1 2 2 3 add(4) splits on root.right == null split

  37. Combined Execution & Splitting 3 3 3 3 3 3 3 2 1 1 2 1 1 3 3 2 1 2 2 3 4 4 3 3 2 4 1 4 1 2 add(4) splits on root.right == null split

  38. Combined Execution & Splitting 3 3 3 3 3 3 3 2 1 1 2 1 1 3 3 2 1 2 2 3 4 4 4 4 3 3 2 1 2 4 1 4 1 3 3 1 2 4 2 4 add(4) splits on root.right == null split splits on root.right.right == null split

  39. Combined Execution & Splitting 3 3 3 3 3 3 3 2 1 1 2 1 1 3 3 2 1 2 2 3 4 4 4 4 4 3 3 2 1 1 2 4 1 4 1 3 3 2 1 2 4 2 4 3 4 add(4) splits on root.right == null split splits on root.right.right == null split

  40. Combined Execution & Splitting 3 3 3 3 3 3 3 2 1 1 2 1 1 3 3 2 1 2 2 3 4 4 4 4 4 3 3 2 1 1 2 4 1 4 1 3 3 2 1 2 4 2 4 3 4 add(4) splits on root.right == null split splits on root.right.right == null split reduction in number of executions: standard has 5, delta has 3

  41. Merging 4 4 4 4 4 3 3 2 1 1 2 4 1 4 1 3 3 2 1 2 4 2 4 3 4 4 4 4 4 4 3 3 2 1 1 2 4 1 4 1 3 3 2 1 2 4 2 4 3 4 merges merge

  42. Split + Merging iteration i Si … … … … … iteration i + 1 Si+1 … • Splits during execution • Merges sets of post-states from execution … …

  43. Efficient ∆Execution • Representation of set of concrete states • Program instrumentation • Optimized state comparison

  44. ∆Execution: State representation 3 3 3 3 3 3 3 2 1 1 2 1 1 3 3 2 1 2 2 3 • Represents a set of concrete states conceptual representation

  45. Representing state: the State 3 3 3 3 3 ∆Objects 3 3 2 1 1 3 3 3 2 1 1

  46. Representing state: the State 3 3 3 3 3 3 3 2 1 1 2 1 1 3 3 3 2 1 1 ∆Objects for references 2 1 1 ? ?

  47. Representing state: the State 3 3 3 3 3 3 3 2 1 1 2 1 1 3 3 2 3 3 3 2 1 1 2 1 1 ? ? ? ? 3 3 2

  48. Representing state: the State 3 3 3 3 3 3 3 2 1 1 2 1 1 3 3 2 1 2 2 3 3 3 3 2 1 1 2 1 1 ? ? ? ? 3 3 2 ? ? ? ? ? ? ? ? 1 2 2 3

  49. Representing state: the State 3 3 3 3 3 3 3 2 1 1 2 1 1 3 3 2 1 2 2 3 ? ? 3 3 2 ? ? ? ? 3 3 3 2 1 1 2 1 1 ? ? ? ? ? ? 1 2 2 3

  50. Constants 3 3 2 1 1 2 1 1 ? ? ? ? 3 3 2 ? ? ? ? ? ? ? ? becomes constant after split due to root.right == null 3 constants created during merging 1 2 2 3

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