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Refinement-Based Termination Proof Tutorial

Learn the basics of refinement-based termination proof methods including variance analysis, well-founded relations, and termination proof rules. Explore recent and future work in this field. Discover strategies for proving termination with linear rank functions. Advantages and disadvantages of this approach are discussed.

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Refinement-Based Termination Proof Tutorial

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  1. Tutorial: Proving termination and liveness Byron Cook Microsoft Research and Queen Mary, Univ. of London

  2. Introduction

  3. Introduction

  4. Introduction

  5. Introduction

  6. Introduction

  7. Introduction

  8. Introduction

  9. Introduction

  10. Outline • Basics • Refinement-based termination proving • Variance analysis • Recent and future work • Conclusion

  11. Outline • Basics • Refinement-based termination proving • Variance analysis • Recent and future work • Conclusion

  12. Well-founded relations =

  13. Well-founded relations =

  14. Well-founded relations =

  15. Well-founded relations

  16. Well-founded relations

  17. Well-founded relations

  18. Well-founded relations

  19. Well-founded relations

  20. Well-founded relations

  21. Well-founded relations

  22. Termination proof rules

  23. Termination proof rules

  24. Termination proof rules

  25. Termination proof rules

  26. Termination proof rules

  27. Termination proof rules

  28. Termination proof rules

  29. Termination proof rules

  30. Termination proof rules

  31. Termination proof rule

  32. Termination proof rule

  33. Termination proof rule

  34. Termination proof rule

  35. Termination proof rule

  36. Termination proof rule

  37. Termination proof rule

  38. Termination proof rule

  39. Termination proof rule

  40. Termination proof rule x := x – y; assume(x>=1); assume(y>=1);

  41. Termination proof rule x := x – y; assume(x>=1); assume(y>=1);

  42. Termination proof rule x := x – y; assume(x>=1); assume(y>=1);

  43. Termination proof rule x := x – y; assume(x>=1); assume(y>=1);

  44. Termination proof rule x := x – y; assume(x>=1); assume(y>=1);

  45. Termination proof rule

  46. Termination proof rule

  47. Outline • Basics • Refinement-based termination proving • Variance analysis • Recent and future work • Conclusion

  48. Outline • Basics • Refinement-based termination proving • Variance analysis • Recent and future work • Conclusion

  49. Outline • Basics • Refinement-based termination proving • Variance analysis • Recent and future work • Conclusion

  50. Refinement • Strategy: • Start with empty termination argument • Iteratively weaken and re-check termination argument • Weaken using linear rank function synthesis • Advantages: • Can use existing safety property checking technology to check argument validity • Finds complex termination arguments with only linear rank functions • Leads to counterexamples • Accurate • Disadvantages: • Very slow • May not terminate (in several ways)

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