communicating recursive programs control and split width
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COMMUNICATING RECURSIVE PROGRAMS: CONTROL AND SPLIT -WIDTH C. - PowerPoint PPT Presentation

Jan 23, 2024 •343 likes •1.67k views

INFORMEL Indo-French Formal Methods Lab COMMUNICATING RECURSIVE PROGRAMS: CONTROL AND SPLIT -WIDTH C. Aiswarya Uppsala University, Sweden Joint work with Paul Gastin K. Narayan Kumar LSV, ENS Cachan, France Chennai Mathematical Institute,

  1. a a c p b d M a c c q b d a a c p b d M ′ a c c q b d p a a c b d M 1 M 2 q c c b d a a a p c b d M ′ 1 M ′ c c q 2 b d a a b d c a M 3 c b d a c a a c b d a c M ′ 3 c b d a split- ! ( n ) ( m, mm ) b d c div- Û Û a c b d TREE INTERPRETATION Vertices

  2. a a c p b d M a c c q b d a a c p b d M ′ a c c q b d p a a c b d M 1 M 2 q c c b d a a a p c b d M ′ 1 M ′ c c q 2 b d a a b d c a M 3 c b d a c a a c b d a c M ′ 3 c b d a split- ! ( n ) ( m, mm ) b d c div- Û Û a c b d TREE INTERPRETATION Vertices

  3. a a c p b d M a c c q b d a a c p b d M ′ a c c q b d p a a c b d M 1 M 2 q c c b d a a a p c b d M ′ 1 M ′ c c q 2 b d a a b d c a M 3 c b d a c a a c b d a c M ′ 3 c b d a split- ! ( n ) ( m, mm ) b d c div- Û Û a c b d TREE INTERPRETATION

  4. a a c p b d M a c c q b d a a c p b d M ′ a c c q b d p a a c b d M 1 M 2 q c c b d a a a p c b d M ′ 1 M ′ c c q 2 b d a a b d c a M 3 c b d a c a a c b d a c M ′ 3 c b d a split- ! ( n ) ( m, mm ) b d c div- Û Û a c b d Data edges TREE INTERPRETATION

  5. a a c p b d M a c c q b d a a c p b d M ′ a c c q b d p a a c b d M 1 M 2 q c c b d a a a p c b d M ′ 1 M ′ c c q 2 b d a a b d c a M 3 c b d a c a a c b d a c M ′ 3 c b d a split- ! ( n ) ( m, mm ) b d c div- Û Û a c b d Data edges TREE INTERPRETATION

  6. a a c p b d M a c c q b d a a c p b d M ′ a c c q b d p a a c b d M 1 M 2 q c c b d a a a p c b d M ′ 1 M ′ c c q 2 b d a 1 a b d c a M 3 c b d a c a a c b d a c M ′ 3 c b d a split- ! ( n ) ( m, mm ) b d c div- Û Û a c b d Data edges TREE INTERPRETATION

  7. a a c p b d M a c c q b d a a c p b d M ′ a c c q b d p a a c b d M 1 M 2 q c c b d a a a p c b d M ′ 1 M ′ c c q 2 b d a a b d c a M 3 c b d a c a a c b d a c M ′ 3 c b d a split- ! ( n ) ( m, mm ) b d c div- Û Û a c b d TREE INTERPRETATION

  8. a a c p b d M a c c q b d a a c p b d M ′ a c c q b d p a a c b d M 1 M 2 q c c b d a a a p c b d M ′ 1 M ′ c c q 2 b d a a b d c a M 3 c b d a c a a c b d a c M ′ 3 c b d a split- ! ( n ) ( m, mm ) b d c div- Û Û a c b d Process edges TREE INTERPRETATION

  9. a a c p b d M a c c q b d a a c p b d M ′ a c c q b d p a a c b d M 1 M 2 q c c b d a a a p c b d M ′ 1 M ′ c c q 2 b d a a b d c a M 3 c b d a c a a c b d a c M ′ 3 c b d a split- ! ( n ) ( m, mm ) b d c div- Û Û a c b d Process edges TREE INTERPRETATION

  10. a a c p b d M a c c q b d a a c p b d M ′ a c c q b d p a a c b d M 1 M 2 q c c b d a a a p c b d M ′ 1 M ′ c c q 2 b d a a b d c a M 3 c b d a c a a c b d a c M ′ 3 c b d a split- ! ( n ) ( m, mm ) b d c div- Û Û a c b d Process edges TREE INTERPRETATION

  11. a a c p b d M a c c q b d a a c p b d M ′ a c c q b d p a a c b d M 1 M 2 q c c b d a a a p c b d M ′ 1 M ′ c c q 2 b d a a b d c a M 3 c b d a c a a c b d a c M ′ 3 c b d a split- ! ( n ) ( m, mm ) b d c div- Û Û a c b d Process edges TREE INTERPRETATION

  12. a a c p b d M a c c q b d a a c p b d M ′ a c c q b d p a a c b d M 1 M 2 q c c b d a a a p c b d M ′ 1 M ′ c c q 2 b d a a b d c a M 3 c b d a c a a c b d a c M ′ 3 c b d a split- ! ( n ) ( m, mm ) b d c div- Û Û a c b d Process edges TREE INTERPRETATION

  13. a a c p b d M a c c q b d a a c p b d M ′ a c c q b d p a a c b d M 1 M 2 q c c b d a a a p c b d M ′ 1 M ′ c c q 2 b d a a b d c a M 3 c b d a c a a c b d a c M ′ 3 c b d a split- ! ( n ) ( m, mm ) b d c div- Û Û a c b d Process edges TREE INTERPRETATION

  14. a a c p b d M a c c q b d a a c p b d M ′ a c c q b d p a a c b d M 1 M 2 q c c b d a a a p c b d M ′ 1 M ′ c c q 2 b d a a b d c a M 3 c b d a c a a c b d a c M ′ 3 c b d a split- ! ( n ) ( m, mm ) b d c div- Û Û a c b d Process edges TREE INTERPRETATION

  15. Split-width Complexity Problem bound on split-width bound on split-width part of the input (in fixed unary) CPDS emptiness ExpTime -Complete PTime -Complete CPDS inclusion or universality ExpTime -Complete 2ExpTime LTL / CPDL satisfiability or model checking ExpTime -Complete ICPDL satisfiability or model checking 2ExpTime -Complete MSO satisfiability or model checking Non-elementary Table 2 Summary of the complexities for bounded split-width verification.

  16. SPLIT-WIDTH Proc 1 Proc 2 Proc 3

  17. SPLIT-WIDTH Proc 1 Proc 2 Proc 3

  18. SPLIT-WIDTH 3 Proc 1 Proc 2 Proc 3

  19. SPLIT-WIDTH 3 Proc 1 Proc 2 Proc 3

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