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Aug 28, 2023 •325 likes •1.72k views

Context Sensitive Dynamic Partial Order Reduction Miguel Gmez-Zamalloa, joint work with Elvira Albert, Puri Arenas, Mara Garca de la Banda, Miguel Isabel, Albert Rubio and Peter Stuckey Introduction Verification and testing on concurrent

  1. DPOR in Action p q r (x = 0) q x = 5; (p 1 ) i = 0; j = 0; p y = x; (q 2 ) z = x; (r 2 ) ‣ Depth-first, stateless traversal starting with an arbitrary q trace ‣ Backtracking points added to backtrack set when q finding reversible races ‣ Sleep set : Events that must not be explored r happens before relation sleep set e backtrack set e and e’ in race final state e’ stopped exploration 5

  2. DPOR in Action p q r (x = 0) q x = 5; (p 1 ) i = 0; j = 0; p y = x; (q 2 ) z = x; (r 2 ) ‣ Depth-first, stateless traversal starting with an arbitrary q trace ‣ Backtracking points added to backtrack set when q finding reversible races ‣ Sleep set : Events that must not be explored r happens before relation sleep set e r backtrack set e and e’ in race final state e’ stopped exploration 5

  3. DPOR in Action p q r (x = 0) q x = 5; (p 1 ) i = 0; j = 0; p y = x; (q 2 ) z = x; (r 2 ) ‣ Depth-first, stateless traversal starting with an arbitrary q trace ‣ Backtracking points added to backtrack set when q finding reversible races ‣ Sleep set : Events that must not be explored r happens before relation sleep set e r backtrack set e and e’ in race final state e’ stopped exploration 5

  4. DPOR in Action p q r (x = 0) q r x = 5; (p 1 ) i = 0; j = 0; p y = x; (q 2 ) z = x; (r 2 ) ‣ Depth-first, stateless traversal starting with an arbitrary q trace ‣ Backtracking points added to backtrack set when q finding reversible races ‣ Sleep set : Events that must not be explored r happens before relation sleep set e r backtrack set e and e’ in race final state e’ stopped exploration 5

  5. DPOR in Action p q r (x = 0) q r x = 5; (p 1 ) i = 0; j = 0; p y = x; (q 2 ) z = x; (r 2 ) ‣ Depth-first, stateless traversal starting with an arbitrary q trace ‣ Backtracking points added to backtrack set when q finding reversible races ‣ Sleep set : Events that must not be explored r happens before relation sleep set e r backtrack set e and e’ in race final state e’ p 1 <q 2 ,p 1 <r 2 stopped exploration y=z=5 5

  6. DPOR in Action p q r (x = 0) q r x = 5; (p 1 ) i = 0; j = 0; p q {p} y = x; (q 2 ) z = x; (r 2 ) ‣ Depth-first, stateless traversal starting with an arbitrary q trace ‣ Backtracking points added to backtrack set when q finding reversible races ‣ Sleep set : Events that must not be explored r happens before relation sleep set e r backtrack set e and e’ in race final state e’ p 1 <q 2 ,p 1 <r 2 stopped exploration y=z=5 5

  7. DPOR in Action p q r (x = 0) q r x = 5; (p 1 ) i = 0; j = 0; p q {p} y = x; (q 2 ) z = x; (r 2 ) ‣ Depth-first, stateless traversal starting with an arbitrary q q trace ‣ Backtracking points added to backtrack set when q finding reversible races ‣ Sleep set : Events that must not be explored r happens before relation sleep set e r backtrack set e and e’ in race final state e’ p 1 <q 2 ,p 1 <r 2 stopped exploration y=z=5 5

  8. DPOR in Action p q r (x = 0) q r x = 5; (p 1 ) i = 0; j = 0; p q {p} y = x; (q 2 ) z = x; (r 2 ) ‣ Depth-first, stateless traversal starting with an arbitrary q q trace ‣ Backtracking points added to backtrack set when q p finding reversible races ‣ Sleep set : Events that must not be explored r happens before relation sleep set e r backtrack set e and e’ in race final state e’ p 1 <q 2 ,p 1 <r 2 stopped exploration y=z=5 5

  9. DPOR in Action p q r (x = 0) q r x = 5; (p 1 ) i = 0; j = 0; p q {p} y = x; (q 2 ) z = x; (r 2 ) ‣ Depth-first, stateless traversal starting with an arbitrary q q trace ‣ Backtracking points added to backtrack set when q p finding reversible races ‣ Sleep set : Events that must not be explored r happens before relation sleep set e r backtrack set e and e’ in race final state e’ p 1 <q 2 ,p 1 <r 2 stopped exploration y=z=5 5

  10. DPOR in Action p q r (x = 0) q r x = 5; (p 1 ) i = 0; j = 0; p q {p} y = x; (q 2 ) z = x; (r 2 ) ‣ Depth-first, stateless traversal starting with an arbitrary q q trace ‣ Backtracking points added to backtrack set when q p finding reversible races ‣ Sleep set : Events that must not be explored r r happens before relation sleep set e r backtrack set e and e’ in race final state e’ p 1 <q 2 ,p 1 <r 2 stopped exploration y=z=5 5

  11. DPOR in Action p q r (x = 0) q r x = 5; (p 1 ) i = 0; j = 0; p q {p} y = x; (q 2 ) z = x; (r 2 ) ‣ Depth-first, stateless traversal starting with an arbitrary q q trace ‣ Backtracking points added to backtrack set when q p finding reversible races ‣ Sleep set : Events that must not be explored r r happens before relation sleep set e r r backtrack set e and e’ in race final state e’ p 1 <q 2 ,p 1 <r 2 stopped exploration y=z=5 5

  12. DPOR in Action p q r (x = 0) q r x = 5; (p 1 ) i = 0; j = 0; p q {p} y = x; (q 2 ) z = x; (r 2 ) ‣ Depth-first, stateless traversal starting with an arbitrary q q trace ‣ Backtracking points added to backtrack set when q p finding reversible races ‣ Sleep set : Events that must not be explored r r happens before relation sleep set e r r backtrack set e and e’ in race final state e’ p 1 <q 2 ,p 1 <r 2 stopped exploration y=z=5 5

  13. DPOR in Action p q r (x = 0) q r x = 5; (p 1 ) i = 0; j = 0; p q {p} y = x; (q 2 ) z = x; (r 2 ) ‣ Depth-first, stateless traversal starting with an arbitrary q q trace r ‣ Backtracking points added to backtrack set when q p finding reversible races ‣ Sleep set : Events that must not be explored r r happens before relation sleep set e r r backtrack set e and e’ in race final state e’ p 1 <q 2 ,p 1 <r 2 stopped exploration y=z=5 5

  14. DPOR in Action p q r (x = 0) q r x = 5; (p 1 ) i = 0; j = 0; p q {p} y = x; (q 2 ) z = x; (r 2 ) ‣ Depth-first, stateless traversal starting with an arbitrary q q trace r ‣ Backtracking points added to backtrack set when q p finding reversible races ‣ Sleep set : Events that must not be explored r r happens before relation sleep set e r r backtrack set e and e’ in race final state e’ p 1 <q 2 ,p 1 <r 2 q 2 <p 1 ,p 1 <r 2 stopped exploration y=z=5 y=0, z=5 5

  15. DPOR in Action p q r (x = 0) q r x = 5; (p 1 ) i = 0; j = 0; p q {p} y = x; (q 2 ) z = x; (r 2 ) ‣ Depth-first, stateless traversal starting with an arbitrary q q trace r ‣ Backtracking points added to backtrack set when r q p finding reversible races {p} ‣ Sleep set : Events that must not be explored r r happens before relation sleep set e r r backtrack set e and e’ in race final state e’ p 1 <q 2 ,p 1 <r 2 q 2 <p 1 ,p 1 <r 2 stopped exploration y=z=5 y=0, z=5 5

  16. DPOR in Action p q r (x = 0) q r x = 5; (p 1 ) i = 0; j = 0; p q {p} y = x; (q 2 ) z = x; (r 2 ) ‣ Depth-first, stateless traversal starting with an arbitrary q q trace r ‣ Backtracking points added to backtrack set when r q p finding reversible races {p} ‣ Sleep set : Events that must not be explored r r r happens before relation sleep set e r r backtrack set e and e’ in race final state e’ p 1 <q 2 ,p 1 <r 2 q 2 <p 1 ,p 1 <r 2 stopped exploration y=z=5 y=0, z=5 5

  17. DPOR in Action p q r (x = 0) q r x = 5; (p 1 ) i = 0; j = 0; p q {p} y = x; (q 2 ) z = x; (r 2 ) ‣ Depth-first, stateless traversal starting with an arbitrary q q trace r ‣ Backtracking points added to backtrack set when r q p finding reversible races {p} ‣ Sleep set : Events that must not be explored r r r happens before relation sleep set e r r p backtrack set e and e’ in race final state e’ p 1 <q 2 ,p 1 <r 2 q 2 <p 1 ,p 1 <r 2 stopped exploration y=z=5 y=0, z=5 5

  18. DPOR in Action p q r (x = 0) q r x = 5; (p 1 ) i = 0; j = 0; p q {p} y = x; (q 2 ) z = x; (r 2 ) ‣ Depth-first, stateless traversal starting with an arbitrary q q trace r ‣ Backtracking points added to backtrack set when r q p finding reversible races {p} ‣ Sleep set : Events that must not be explored r r r happens before relation sleep set e r r p backtrack set e and e’ in race final state e’ p 1 <q 2 ,p 1 <r 2 q 2 <p 1 ,p 1 <r 2 stopped exploration y=z=5 y=0, z=5 5

  19. DPOR in Action p q r (x = 0) q r x = 5; (p 1 ) i = 0; j = 0; p q {p} y = x; (q 2 ) z = x; (r 2 ) r ‣ Depth-first, stateless traversal starting with an arbitrary q q trace r ‣ Backtracking points added to backtrack set when r q p finding reversible races {p} ‣ Sleep set : Events that must not be explored r r r happens before relation sleep set e r r p backtrack set e and e’ in race final state e’ p 1 <q 2 ,p 1 <r 2 q 2 <p 1 ,p 1 <r 2 q 2 <p 1 ,r 2 <p 1 stopped exploration y=z=5 y=0, z=5 y=z=0 5

  20. DPOR in Action p q r (x = 0) q r x = 5; (p 1 ) i = 0; j = 0; p q {p} y = x; (q 2 ) z = x; (r 2 ) r ‣ Depth-first, stateless traversal starting with an arbitrary r q q trace {p,q} r ‣ Backtracking points added to backtrack set when r q p finding reversible races {p} ‣ Sleep set : Events that must not be explored r r r happens before relation sleep set e r r p backtrack set e and e’ in race final state e’ p 1 <q 2 ,p 1 <r 2 q 2 <p 1 ,p 1 <r 2 q 2 <p 1 ,r 2 <p 1 stopped exploration y=z=5 y=0, z=5 y=z=0 5

  21. DPOR in Action p q r (x = 0) q r x = 5; (p 1 ) i = 0; j = 0; p q {p} y = x; (q 2 ) z = x; (r 2 ) r ‣ Depth-first, stateless traversal starting with an arbitrary r q q trace {p,q} r ‣ Backtracking points added to backtrack set when r q p finding reversible races r {p} {q} ‣ Sleep set : Events that must not be explored r r r happens before relation sleep set e r r p backtrack set e and e’ in race final state e’ p 1 <q 2 ,p 1 <r 2 q 2 <p 1 ,p 1 <r 2 q 2 <p 1 ,r 2 <p 1 stopped exploration y=z=5 y=0, z=5 y=z=0 5

  22. DPOR in Action p q r (x = 0) q r x = 5; (p 1 ) i = 0; j = 0; p q {p} y = x; (q 2 ) z = x; (r 2 ) r ‣ Depth-first, stateless traversal starting with an arbitrary r q q trace {p,q} r ‣ Backtracking points added to backtrack set when r q p finding reversible races r {p} {q} ‣ Sleep set : Events that must not be explored r r r p happens before relation sleep set e q r r p backtrack set e and e’ in race final state e’ p 1 <q 2 ,p 1 <r 2 q 2 <p 1 ,p 1 <r 2 q 2 <p 1 ,r 2 <p 1 r 2 <p 1 ,p 1 <q 2 stopped exploration y=5, z=0 y=z=5 y=0, z=5 y=z=0 5

  23. DPOR in Action p q r (x = 0) q r x = 5; (p 1 ) i = 0; j = 0; p q r {p} {p,q} y = x; (q 2 ) z = x; (r 2 ) r ‣ Depth-first, stateless traversal starting with an arbitrary r q q trace {p,q} r ‣ Backtracking points added to backtrack set when r q p finding reversible races r {p} {q} ‣ Sleep set : Events that must not be explored r r r p happens before relation sleep set e q r r p backtrack set e and e’ in race final state e’ p 1 <q 2 ,p 1 <r 2 q 2 <p 1 ,p 1 <r 2 q 2 <p 1 ,r 2 <p 1 r 2 <p 1 ,p 1 <q 2 stopped exploration y=5, z=0 y=z=5 y=0, z=5 y=z=0 5

  24. DPOR in Action p q r (x = 0) q r x = 5; (p 1 ) i = 0; j = 0; p q r {p} {p,q} y = x; (q 2 ) z = x; (r 2 ) r ‣ Depth-first, stateless traversal starting with an arbitrary r q q r trace {q} {p,q} r ‣ Backtracking points added to backtrack set when r q p finding reversible races r {p} {q} ‣ Sleep set : Events that must not be explored r r r p happens before relation sleep set e q r r p backtrack set e and e’ in race final state e’ p 1 <q 2 ,p 1 <r 2 q 2 <p 1 ,p 1 <r 2 q 2 <p 1 ,r 2 <p 1 r 2 <p 1 ,p 1 <q 2 stopped exploration y=5, z=0 y=z=5 y=0, z=5 y=z=0 5

  25. DPOR in Action p q r (x = 0) q r x = 5; (p 1 ) i = 0; j = 0; p q r {p} {p,q} y = x; (q 2 ) z = x; (r 2 ) r ‣ Depth-first, stateless traversal starting with an arbitrary r q q r trace {q} {p,q} r ‣ Backtracking points added to backtrack set when r q p finding reversible races p r {p} {q} ‣ Sleep set : Events that must not be explored r r r p happens before relation sleep set e q r r p backtrack set e and e’ in race final state e’ p 1 <q 2 ,p 1 <r 2 q 2 <p 1 ,p 1 <r 2 q 2 <p 1 ,r 2 <p 1 r 2 <p 1 ,p 1 <q 2 stopped exploration y=5, z=0 y=z=5 y=0, z=5 y=z=0 5

  26. DPOR in Action p q r (x = 0) q r x = 5; (p 1 ) i = 0; j = 0; p q r {p} {p,q} y = x; (q 2 ) z = x; (r 2 ) r ‣ Depth-first, stateless traversal starting with an arbitrary r q q r trace {q} {p,q} r ‣ Backtracking points added to backtrack set when r q p finding reversible races p r {p} {q} ‣ Sleep set : Events that must not be explored r r r p happens before relation sleep set e q r r p backtrack set e and e’ in race final state e’ p 1 <q 2 ,p 1 <r 2 q 2 <p 1 ,p 1 <r 2 q 2 <p 1 ,r 2 <p 1 r 2 <p 1 ,p 1 <q 2 stopped exploration y=5, z=0 y=z=5 y=0, z=5 y=z=0 5

  27. DPOR in Action p q r (x = 0) q r x = 5; (p 1 ) i = 0; j = 0; p q r {p} {p,q} y = x; (q 2 ) z = x; (r 2 ) r ‣ Depth-first, stateless traversal starting with an arbitrary r q q r trace {q} {p,q} r ‣ Backtracking points added to backtrack set when r q p finding reversible races p r {p} {q} {q} ‣ Sleep set : Events that must not be explored ‣ Some explored sequences eventually cut by sleep sets r r r p happens before relation sleep set e q r r p backtrack set e and e’ in race final state e’ p 1 <q 2 ,p 1 <r 2 q 2 <p 1 ,p 1 <r 2 q 2 <p 1 ,r 2 <p 1 r 2 <p 1 ,p 1 <q 2 stopped exploration y=5, z=0 y=z=5 y=0, z=5 y=z=0 5

  28. Optimal* DPOR in Action (* without wake-up trees) x = 0 p q r x = 5; (p 1 ) i = 0; j = 0; y = x; (q 2 ) z = x; (r 2 ) happens before relation e sleep set backtrack set e and e’ in race e’ Final state 6

  29. Optimal* DPOR in Action (* without wake-up trees) x = 0 q p q r x = 5; (p 1 ) i = 0; j = 0; p y = x; (q 2 ) z = x; (r 2 ) q q r happens before relation e sleep set backtrack set e and e’ in race e’ Final state 6

  30. Optimal* DPOR in Action (* without wake-up trees) x = 0 q p q r x = 5; (p 1 ) i = 0; j = 0; p y = x; (q 2 ) z = x; (r 2 ) q q r happens before relation e sleep set backtrack set e and e’ in race r e’ Final state 6

  31. Optimal* DPOR in Action (* without wake-up trees) x = 0 q p q r x = 5; (p 1 ) i = 0; j = 0; p y = x; (q 2 ) z = x; (r 2 ) q q r happens before relation e sleep set backtrack set e and e’ in race r e’ Final state 6

  32. Optimal* DPOR in Action (* without wake-up trees) x = 0 q p q r r x = 5; (p 1 ) i = 0; j = 0; p y = x; (q 2 ) z = x; (r 2 ) q ‣ No need to backtrack with r in the initial state! ‣ It prevents sleep set blocked explorations q ‣ E.g., with 8 readers it explores 256 traces vs. 3281! r happens before relation e sleep set backtrack set e and e’ in race r e’ Final state 6

  33. Optimal* DPOR in Action (* without wake-up trees) x = 0 q p q r r x = 5; (p 1 ) i = 0; j = 0; p y = x; (q 2 ) z = x; (r 2 ) q ‣ No need to backtrack with r in the initial state! ‣ It prevents sleep set blocked explorations q ‣ E.g., with 8 readers it explores 256 traces vs. 3281! r happens before relation e sleep set backtrack set e and e’ in race r e’ Final state p 1 <q 2 ,p 1 <r 2 y=z=5 6

  34. Optimal* DPOR in Action (* without wake-up trees) x = 0 q p q r r x = 5; (p 1 ) i = 0; j = 0; p q r {p} {p,q} y = x; (q 2 ) z = x; (r 2 ) r r q q r {q} {p} ‣ No need to backtrack with r in the initial state! r ‣ It prevents sleep set blocked explorations r q p p r ‣ E.g., with 8 readers it explores 256 traces vs. 3281! {p} {q} r r r p happens before relation e sleep set backtrack set e and e’ in race q r r p e’ Final state q 2 <p 1 ,p 1 <r 2 q 2 <p 1 ,r 2 <p 1 r 2 <p 1 ,p 1 <q 2 p 1 <q 2 ,p 1 <r 2 y=5, z=0 y=z=5 y=0, z=5 y=z=0 6

  35. There is Room for Improvement: Dep. over-approx. ‣ DPOR requires over-approximating dependencies (e.g same var. and at least one writes) ‣ Using the traditional dependence approx., all p,q,r are dependent to each other ‣ Hence all six orders must be explored Consider another example: q p r (x = 0) x = 5; x = 5; y = x; p q p q r r q p r r p q r r q p q p 7

  36. There is Room for Improvement: Dep. over-approx. ‣ DPOR requires over-approximating dependencies (e.g same var. and at least one writes) ‣ Using the traditional dependence approx., all p,q,r are dependent to each other ‣ Hence all six orders must be explored ‣ But p and q are indeed independent Consider another example: q p r (x = 0) x = 5; x = 5; y = x; p q p q r r q p r r p q r r q p q p = = 7

  37. There is Room for Improvement: Dep. over-approx. ‣ DPOR requires over-approximating dependencies (e.g same var. and at least one writes) ‣ Using the traditional dependence approx., all p,q,r are dependent to each other ‣ Hence all six orders must be explored ‣ But p and q are indeed independent Consider another example: q p r (x = 0) x = 5; x = 5; y = x; p q p q r r q p r r p q r r q p q p = = ‣ With an exact dep. approximation it needs to explore 4, but ... 7

  38. There is Room for Improvement: Dep. over-approx. ‣ DPOR requires over-approximating dependencies (e.g same var. and at least one writes) ‣ Using the traditional dependence approx., all p,q,r are dependent to each other ‣ Hence all six orders must be explored ‣ But p and q are indeed independent Consider another example: q p r (x = 0) x = 5; x = 5; y = x; p q p q r r ‣ It could be more tricky: q p r r p q p q r x++; y = x; x--; r r q p q p = = ‣ With an exact dep. approximation it needs to explore 4, but ... 7

  39. There is Room for Improvement: Dep. over-approx. ‣ DPOR requires over-approximating dependencies (e.g same var. and at least one writes) ‣ Using the traditional dependence approx., all p,q,r are dependent to each other ‣ Hence all six orders must be explored ‣ But p and q are indeed independent Consider another example: q p r (x = 0) x = 5; x = 5; y = x; p q p q r r ‣ It could be more tricky: q p r r p q p q r x++; y = x; x--; r r q p q p ‣ And much more with bigger atomic sections = = ‣ With an exact dep. approximation it needs to explore 4, but ... 7

  40. There is Room for Improvement: Sensitivity to Context ‣ Observe that there are only two outcomes: y = 0 or y = 5 ‣ q and r (and also p and r) are independent in the context x = 5 ‣ Only two orders need to be explored p q r (x = 0) x = 5; x = 5; y = x; p q p q r r q p r r p q r r q p q p 8

  41. There is Room for Improvement: Sensitivity to Context ‣ Observe that there are only two outcomes: y = 0 or y = 5 ‣ q and r (and also p and r) are independent in the context x = 5 ‣ Only two orders need to be explored p q r (x = 0) x = 5; x = 5; y = x; p q p q r r q p r r p q r r q p q p = = 8

  42. There is Room for Improvement: Sensitivity to Context ‣ Observe that there are only two outcomes: y = 0 or y = 5 ‣ q and r (and also p and r) are independent in the context x = 5 ‣ Only two orders need to be explored p q r (x = 0) x = 5; x = 5; y = x; p q p q r r q p r r p q r r q p q p = = (r < p and r < q) leads to y = 0 (p < r or q < r) leads to y = 5 8

  43. Context Sensitive DPOR 1.0 [CAV’17] ‣ Refinement over Optimal* DPOR (* without wake-up trees) ‣ It computes exact (in)dependencies overcoming the loss of precision of (in)dependency over-approximations ‣ It takes advantage of context-sensitive dependencies ‣ It adds a new check in the race detection phase ‣ If it succeeds it adds a sequence to the corresponding sleep-set ‣ Sleep-sets can now include sequences and are propagated accordingly ‣ The exploration can only get reduced 9

  44. Context Sensitive DPOR 1.0 in Action p q r x = 5; x = 5; y = x; happens before relation r r r p p p p added to p already in p in sleep backtrack set backtrack set sleep set backtrack new sleep set entries Final state Reduced explorations 10

  45. Context Sensitive DPOR 1.0 in Action p q r x = 5; x = 5; y = x; p happens before relation r r r p p p p added to p already in p in sleep backtrack set backtrack set sleep set backtrack new sleep set entries Final state Reduced explorations 10

  46. Context Sensitive DPOR 1.0 in Action p q r x = 5; x = 5; y = x; p happens before relation r r r q p p p p added to p already in p in sleep backtrack set backtrack set sleep set backtrack new sleep set entries Final state Reduced explorations 10

  47. Context Sensitive DPOR 1.0 in Action p q r x = 5; x = 5; y = x; p happens before relation r r r q p p p p added to p already in p in sleep backtrack set backtrack set sleep set backtrack new sleep set entries Final state Reduced explorations 10

  48. Context Sensitive DPOR 1.0 in Action p q r q x = 5; x = 5; y = x; p happens before relation r r r q p p p p added to p already in p in sleep backtrack set backtrack set sleep set backtrack new sleep set entries Final state Reduced explorations 10

  49. Context Sensitive DPOR 1.0 in Action p q r q x = 5; x = 5; y = x; p happens before relation r r r p.q = q.p q p p p p added to p already in p in sleep backtrack set backtrack set sleep set backtrack new sleep set entries Final state Reduced explorations 10

  50. Context Sensitive DPOR 1.0 in Action p q r q {q.p} x = 5; x = 5; y = x; p happens before relation r r r p.q = q.p q p p p p added to p already in p in sleep backtrack set backtrack set sleep set backtrack new sleep set entries Final state Reduced explorations 10

  51. Context Sensitive DPOR 1.0 in Action p q r q {q.p} x = 5; x = 5; y = x; p happens before relation r r r q p p p p added to p already in p in sleep backtrack set backtrack set sleep set backtrack new sleep set entries Final state Reduced explorations 10

  52. Context Sensitive DPOR 1.0 in Action p q r q {q.p} x = 5; x = 5; y = x; p happens before relation r r r q p p p p added to p already in p in sleep r backtrack set backtrack set sleep set backtrack new sleep set entries Final state Reduced explorations 10

  53. Context Sensitive DPOR 1.0 in Action p q r q {q.p} x = 5; x = 5; y = x; p happens before relation r r r q p p p p added to p already in p in sleep r backtrack set backtrack set sleep set backtrack new sleep set entries Final state Reduced explorations 10

  54. Context Sensitive DPOR 1.0 in Action p q r q {q.p} x = 5; x = 5; y = x; p happens before relation r r r r q p p p p added to p already in p in sleep r backtrack set backtrack set sleep set backtrack new sleep set entries Final state Reduced explorations 10

  55. Context Sensitive DPOR 1.0 in Action p q r q {q.p} x = 5; x = 5; y = x; p happens before relation r r r r q p p p p added to p already in p in sleep r p.q.r = p.r.q backtrack set backtrack set sleep set backtrack new sleep set entries Final state Reduced explorations 10

  56. Context Sensitive DPOR 1.0 in Action p q r q {q.p} x = 5; x = 5; y = x; p happens before relation r {r.q} r r r q p p p p added to p already in p in sleep r p.q.r = p.r.q backtrack set backtrack set sleep set backtrack new sleep set entries Final state Reduced explorations 10

  57. Context Sensitive DPOR 1.0 in Action p q r q {q.p} x = 5; x = 5; y = x; p happens before relation r {r.q} r r r q p p p p added to p already in p in sleep r backtrack set backtrack set sleep set backtrack new sleep set entries Final state Reduced explorations 10

  58. Context Sensitive DPOR 1.0 in Action p q r q {q.p} x = 5; x = 5; y = x; p happens before relation r {r.q} r r r q p p p p added to p already in p in sleep r backtrack set backtrack set sleep set p.q.r backtrack new sleep y=5 set entries Final state Reduced explorations 10

  59. Context Sensitive DPOR 1.0 in Action p q r q {q.p} x = 5; x = 5; y = x; p happens before relation r {r.q} r r r r q {q} p p p p added to p already in p in sleep r backtrack set backtrack set sleep set p.q.r backtrack new sleep y=5 set entries Final state Reduced explorations 10

  60. Context Sensitive DPOR 1.0 in Action p q r q {q.p} x = 5; x = 5; y = x; p happens before relation r {r.q} r r r r q {q} p p p p added to p already in p in sleep r backtrack set backtrack set sleep set p.q.r backtrack new sleep y=5 set entries Final state Reduced explorations 10

  61. Context Sensitive DPOR 1.0 in Action p q r q r {q.p} x = 5; x = 5; y = x; p happens before relation r {r.q} r r r r q {q} p p p p added to p already in p in sleep r backtrack set backtrack set sleep set p.q.r backtrack new sleep y=5 set entries Final state Reduced explorations 10

  62. Context Sensitive DPOR 1.0 in Action p q r q r {q.p} x = 5; x = 5; y = x; p happens before relation r {r.q} r r r p.r ≠ r.p r q {q} p p p p added to p already in p in sleep r backtrack set backtrack set sleep set p.q.r backtrack new sleep y=5 set entries Final state Reduced explorations 10

  63. Context Sensitive DPOR 1.0 in Action p q r q r {q.p} x = 5; x = 5; y = x; p happens before relation r {r.q} r r r r q {q} p p p p added to p already in p in sleep r backtrack set backtrack set sleep set p.q.r backtrack new sleep y=5 set entries Final state Reduced explorations 10

  64. Context Sensitive DPOR 1.0 in Action p q r q r {q.p} x = 5; x = 5; y = x; q p happens before relation r {r.q} r r r r q {q} p p p p added to p already in p in sleep r backtrack set backtrack set sleep set p.q.r backtrack new sleep y=5 set entries Final state Reduced explorations 10

  65. Context Sensitive DPOR 1.0 in Action p q r q r {q.p} x = 5; x = 5; y = x; q p {p} happens before relation r {r.q} r r r r q {q} p p p p added to p already in p in sleep r backtrack set backtrack set sleep set p.q.r backtrack new sleep y=5 set entries Final state Reduced explorations 10

  66. Context Sensitive DPOR 1.0 in Action p q r q r {q.p} x = 5; x = 5; y = x; q p {p} happens before relation r {r.q} r r r r r q {q} p p p p added to p already in p in sleep r backtrack set backtrack set sleep set p.q.r backtrack new sleep y=5 set entries Final state Reduced explorations 10

  67. Context Sensitive DPOR 1.0 in Action p q r q r {q.p} x = 5; x = 5; y = x; q p {p} happens before relation r {r.q} r r r r r q {q} p p p p added to p already in p in sleep r backtrack set backtrack set sleep set p.q.r backtrack new sleep y=5 set entries Final state Reduced explorations 10

  68. Context Sensitive DPOR 1.0 in Action p q r q r {q.p} x = 5; x = 5; y = x; q p {p} happens before relation r {r.q} r r r r r q.r ≠ r.q q {q} p p p p added to p already in p in sleep r backtrack set backtrack set sleep set p.q.r backtrack new sleep y=5 set entries Final state Reduced explorations 10

  69. Context Sensitive DPOR 1.0 in Action p q r q r {q.p} x = 5; x = 5; y = x; q p {p} happens before relation r {r.q} r r r r r q {q} p p p p added to p already in p in sleep r p backtrack set backtrack set sleep set p.q.r backtrack new sleep y=5 set entries Final state Reduced explorations 10

  70. Context Sensitive DPOR 1.0 in Action p q r q r {q.p} x = 5; x = 5; y = x; q p {p} happens before relation r {r.q} r r r r r q {q} p p p p added to p already in p in sleep r p backtrack set backtrack set sleep set p.q.r q.r.p backtrack new sleep y=5 y=5 set entries Final state Reduced explorations 10

  71. Context Sensitive DPOR 1.0 in Action p q r q r {q.p} x = 5; x = 5; y = x; q p {p} happens before relation r {r.q} r r r r r q {q} p p p p added to p already in p in sleep r p backtrack set backtrack set sleep set p.q.r q.r.p backtrack new sleep y=5 y=5 set entries Final state Reduced explorations 10

  72. Context Sensitive DPOR 1.0 in Action p q r q r {q.p} x = 5; x = 5; y = x; r q p {p} happens before relation r {r.q} r r r r r q {q} p p p p added to p already in p in sleep r p backtrack set backtrack set sleep set p.q.r q.r.p backtrack new sleep y=5 y=5 set entries Final state Reduced explorations 10

  73. Context Sensitive DPOR 1.0 in Action p q r q r {q.p} x = 5; x = 5; y = x; r q p {p} happens before relation r {r.q} r r r r p r q {q} p p p p added to p already in p in sleep r p backtrack set backtrack set sleep set p.q.r q.r.p backtrack new sleep y=5 y=5 set entries Final state Reduced explorations 10

  74. Context Sensitive DPOR 1.0 in Action p q r q r {q.p} x = 5; x = 5; y = x; r q p {p} happens before relation r {r.q} r r r r p r q {q} p p p p added to p already in p in sleep r p backtrack set backtrack set sleep set p.q.r q.r.p backtrack new sleep y=5 y=5 set entries Final state Reduced explorations 10

  75. Context Sensitive DPOR 1.0 in Action p q r q r {q.p} x = 5; x = 5; y = x; r q p {p} happens before relation r {r.q} r r r r p r q {q} p p p p added to p already in p in sleep r p q backtrack set backtrack set sleep set p.q.r q.r.p backtrack new sleep y=5 y=5 set entries Final state Reduced explorations 10

  76. Context Sensitive DPOR 1.0 in Action p q r q r {q.p} x = 5; x = 5; y = x; r q p {p} happens before relation r {r.q} r r r r p r q {q} p p p p added to p already in p in sleep r p q backtrack set backtrack set sleep set p.q.r q.r.p backtrack new sleep y=5 y=5 set entries Final state Reduced explorations 10

  77. Context Sensitive DPOR 1.0 in Action p q r q r {q.p} x = 5; x = 5; y = x; r q p {p} happens before relation q r {r.q} r r r r p r q {q} p p p p added to p already in p in sleep r p q backtrack set backtrack set sleep set p.q.r q.r.p backtrack new sleep y=5 y=5 set entries Final state Reduced explorations 10

  78. Context Sensitive DPOR 1.0 in Action p q r q r {q.p} x = 5; x = 5; y = x; r q p {p} happens before relation q {q.p} r {r.q} r r r r p r q {q} p p p p added to p already in p in sleep r p q r.p.q = r.q.p backtrack set backtrack set sleep set p.q.r q.r.p backtrack new sleep y=5 y=5 set entries Final state Reduced explorations 10

  79. Context Sensitive DPOR 1.0 in Action p q r q r {q.p} x = 5; x = 5; y = x; r q p {p} happens before relation q {q.p} r {r.q} r r r r p r q {q} p p p p added to p already in p in sleep r p q backtrack set backtrack set sleep set p.q.r q.r.p r.p.q backtrack new sleep y=5 y=5 y=0 set entries Final state Reduced explorations 10

  80. Context Sensitive DPOR 1.0 in Action p q r q r {q.p} x = 5; x = 5; y = x; r q p {p} happens before relation q {q.p} r {r.q} r r r q r p r q {q} p p p p added to p already in p in sleep r p q backtrack set backtrack set sleep set p.q.r q.r.p r.p.q backtrack new sleep y=5 y=5 y=0 set entries Final state Reduced explorations 10

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