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Games and Automata: From Boolean to Quantitative Verification

Games and Automata: From Boolean to Quantitative Verification. - Habilitation thesis defense -. Laurent Doyen CNRS. ENS Cachan, March 13th, 2012. Outline. Antichain Algorithms Finite automata, Büchi automata, alternating automata, partial-observation games, QBF

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Games and Automata: From Boolean to Quantitative Verification

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  1. Games and Automata:From Boolean to Quantitative Verification - Habilitation thesis defense - Laurent DoyenCNRS ENS Cachan, March 13th, 2012

  2. Outline • Antichain Algorithms • Finite automata, Büchi automata, alternating automata, partial-observation games, QBF • Quantitative Games • Energy games, mean-payoff games, partial- observation, energy parity, multi-dimension • Quantitative Languages • Automata-based model, complexity, expressiveness, closure properties, mean-payoff automaton expression Context and perspective of a selection of results

  3. Model-checking Check if a Model satisfies a Property ? …in an automated way [Clarke, Emerson, Pnueli, Sifakis,...]

  4. Model-checking What kind of properties ?

  5. Model-checking What kind of properties ? Avoid failures !

  6. Model-checking What kind of properties ? Ensure responsiveness !

  7. Model-checking What kind of models ?

  8. Model-checking What kind of models ? • Reactive systems: • Non-terminating • Safety-critical • Data abstraction

  9. Model-checking

  10. Example grant Server Clients request

  11. Example g {g1,g2} Server 1 1 2 r {r1,r2}

  12. Example « Every request is eventually granted, no simultaneous grants » g {g1,g2} Server 1 1 2 r {r1,r2}

  13. Example « Every request is eventually granted, no simultaneous grants » g {g1,g2} Server 1 1 2 r {r1,r2} ω-automaton

  14. Example « Every request is eventually granted, no simultaneous grants » g {g1,g2} Server 1 1 2 r {r1,r2} Closure properties Expressiveness Decidability ω-automaton

  15. Example « Every request is eventually granted, no simultaneous grants » g {g1,g2} Server 1 1 2 r {r1,r2} Closure properties Expressiveness Decidability Translation to automata ω-automaton LTL

  16. Example « Every request is eventually granted, no simultaneous grants » g {g1,g2} Server 1 1 2 r {r1,r2} Closure properties Expressiveness Decidability Translation to automata ω-automaton Trace inclusion LTL Yes/No answer

  17. Example « Every request is eventually granted, no simultaneous grants » g {g1,g2} Server 1 1 2 r {r1,r2} Closure properties Expressiveness Decidability Translation to automata ω-automaton Trace inclusion LTL Yes/No answer Automata-based approach to model-checking [Vardi, Wolper,...]

  18. Outline From Boolean to quantitative verification

  19. Outline From Boolean to quantitative verification • Boolean automata-based Verification • 1. Techniques to speed up well-known verification algorithms by orders of magnitude • Quantitative Verification • 2. A surprising complexity result in game theory • 3. A robust and decidable class of quantitative languages • -

  20. Algorithm ?

  21. Algorithm ? Translation to automata

  22. Algorithm ? Translation to automata Closure properties

  23. Algorithm ? Translation to automata Closure properties This problem is PSPACE-complete

  24. Algorithm ? Translation to automata Closure properties This problem is PSPACE-complete even if is given explicitly, even over finite words, and even if

  25. Efficient Algorithm ?

  26. Efficient Algorithm ? Subset construction

  27. Subset Construction

  28. Subset Construction

  29. Subset Construction

  30. Subset Construction . . . .

  31. Subset Construction . . . .

  32. Subset Construction . . . . . . . .

  33. Subset Construction . . . . . . . .

  34. Subset Construction . . . . . . . . Pruning is sound: either or

  35. Subset Construction . . . . . . . . Pruning is sound: either or

  36. Subset Construction

  37. Subset Construction

  38. Subset Construction

  39. Reachability Final Init Is there a (finite) path from Init to Final ?

  40. Reachability Is there a (finite) path from Init to Final ?

  41. Structure in graphs Final Init

  42. Structure in graphs Final Init Graph is partially ordered…

  43. Structure in graphs Final Init Final Graph is monotone…

  44. Structure in graphs . . . . Key property . . . .

  45. Structure in graphs . . . . Key property . . . . Two interpretations: • is a forward simulation relation in Ac • is a backward simulation relation in Ac

  46. Structure in graphs . . . . Key property . . . . Two interpretations: • is a forward simulation relation in Ac Use  to prune the search

  47. Structure in graphs . . . . Key property . . . . Two interpretations: • is a forward simulation relation in Ac Use  to prune the search

  48. Structure in graphs . . . . Key property . . . . Two interpretations: • is a forward simulation relation in Ac Use  to prune the search

  49. Structure in graphs . . . . Key property . . . . Two interpretations: • is a forward simulation relation in Ac Use  to prune the search

  50. Structure in graphs . . . . Key property . . . . Two interpretations: • is a forward simulation relation in Ac Use  to prune the search

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