Synthesis in Multi-Criteria Quantitative Games Mickael Randour - PowerPoint PPT Presentation

Synthesis in Multi-Criteria Quantitative Games Mickael Randour Advisors: V´ eronique Bruy` ere & Jean-Fran¸ cois Raskin Mons - 18.04.2014 Private PhD Thesis Defense

Quantitative Games Beyond Worst-Case Synthesis Multi-Dimension Objectives Window Objectives Conclusion 1 Synthesis in Quantitative Games 2 Beyond Worst-Case Synthesis 3 Multi-Dimension Objectives 4 Window Objectives 5 Conclusion and Future Work Synthesis in Multi-Criteria Quantitative Games M. Randour (advisors: V. Bruy` ere & J.-F. Raskin) 1 / 34

Quantitative Games Beyond Worst-Case Synthesis Multi-Dimension Objectives Window Objectives Conclusion 1 Synthesis in Quantitative Games 2 Beyond Worst-Case Synthesis 3 Multi-Dimension Objectives 4 Window Objectives 5 Conclusion and Future Work Synthesis in Multi-Criteria Quantitative Games M. Randour (advisors: V. Bruy` ere & J.-F. Raskin) 2 / 34

Quantitative Games Beyond Worst-Case Synthesis Multi-Dimension Objectives Window Objectives Conclusion General context Verification and synthesis: � a reactive system to control , � an interacting environment , � a specification to enforce . Synthesis in Multi-Criteria Quantitative Games M. Randour (advisors: V. Bruy` ere & J.-F. Raskin) 3 / 34

Quantitative Games Beyond Worst-Case Synthesis Multi-Dimension Objectives Window Objectives Conclusion General context Verification and synthesis: � a reactive system to control , � an interacting environment , � a specification to enforce . Qualitative and quantitative specifications. Synthesis in Multi-Criteria Quantitative Games M. Randour (advisors: V. Bruy` ere & J.-F. Raskin) 3 / 34

Quantitative Games Beyond Worst-Case Synthesis Multi-Dimension Objectives Window Objectives Conclusion General context Verification and synthesis: � a reactive system to control , � an interacting environment , � a specification to enforce . Qualitative and quantitative specifications. Focus on multi-criteria quantitative models � to reason about trade-offs and interplays . Synthesis in Multi-Criteria Quantitative Games M. Randour (advisors: V. Bruy` ere & J.-F. Raskin) 3 / 34

Quantitative Games Beyond Worst-Case Synthesis Multi-Dimension Objectives Window Objectives Conclusion Synthesis via two-player graph games system environment informal description description specification model as model as winning a game objectives synthesis is there a winning strategy ? no yes empower system capabilities strategy = or weaken controller specification requirements Synthesis in Multi-Criteria Quantitative Games M. Randour (advisors: V. Bruy` ere & J.-F. Raskin) 4 / 34

Quantitative Games Beyond Worst-Case Synthesis Multi-Dimension Objectives Window Objectives Conclusion Synthesis via two-player graph games system environment informal description description specification model as model as winning a game objectives 1 Can one player guarantee victory? synthesis is there a winning strategy ? no yes empower system capabilities strategy = or weaken controller specification requirements Synthesis in Multi-Criteria Quantitative Games M. Randour (advisors: V. Bruy` ere & J.-F. Raskin) 4 / 34

Quantitative Games Beyond Worst-Case Synthesis Multi-Dimension Objectives Window Objectives Conclusion Synthesis via two-player graph games system environment informal description description specification model as model as winning a game objectives 1 Can one player guarantee victory? synthesis 2 Can we decide which one? is there a winning strategy ? no yes empower system capabilities strategy = or weaken controller specification requirements Synthesis in Multi-Criteria Quantitative Games M. Randour (advisors: V. Bruy` ere & J.-F. Raskin) 4 / 34

Quantitative Games Beyond Worst-Case Synthesis Multi-Dimension Objectives Window Objectives Conclusion Synthesis via two-player graph games system environment informal description description specification model as model as winning a game objectives 1 Can one player guarantee victory? synthesis 2 Can we decide which one? 3 How complex his strategy is there a needs to be? winning strategy ? no yes empower system capabilities strategy = or weaken controller specification requirements Synthesis in Multi-Criteria Quantitative Games M. Randour (advisors: V. Bruy` ere & J.-F. Raskin) 4 / 34

Quantitative Games Beyond Worst-Case Synthesis Multi-Dimension Objectives Window Objectives Conclusion Quantitative games on graphs Graph G = ( S , E , w ) with w : E → Z Deterministic transitions Two-player game G = ( G , S 1 , S 2 ) 2 2 � P 1 states = � P 2 states = 5 Plays have values � f : Plays( G ) → R ∪ {−∞ , ∞} − 1 7 − 4 Players follow strategies � λ i : Prefs i ( G ) → D ( S ) � Finite memory ⇒ stochastic output Moore machine M ( λ i ) = (Mem , m 0 , α u , α n ) Synthesis in Multi-Criteria Quantitative Games M. Randour (advisors: V. Bruy` ere & J.-F. Raskin) 5 / 34

Quantitative Games Beyond Worst-Case Synthesis Multi-Dimension Objectives Window Objectives Conclusion Quantitative games on graphs Graph G = ( S , E , w ) with w : E → Z Deterministic transitions Two-player game G = ( G , S 1 , S 2 ) 2 2 � P 1 states = � P 2 states = 5 Plays have values � f : Plays( G ) → R ∪ {−∞ , ∞} − 1 7 − 4 Players follow strategies � λ i : Prefs i ( G ) → D ( S ) � Finite memory ⇒ stochastic output Moore machine M ( λ i ) = (Mem , m 0 , α u , α n ) Synthesis in Multi-Criteria Quantitative Games M. Randour (advisors: V. Bruy` ere & J.-F. Raskin) 5 / 34

Quantitative Games Beyond Worst-Case Synthesis Multi-Dimension Objectives Window Objectives Conclusion Quantitative games on graphs Graph G = ( S , E , w ) with w : E → Z Deterministic transitions Two-player game G = ( G , S 1 , S 2 ) 2 2 � P 1 states = � P 2 states = 5 Plays have values � f : Plays( G ) → R ∪ {−∞ , ∞} − 1 7 − 4 Players follow strategies � λ i : Prefs i ( G ) → D ( S ) � Finite memory ⇒ stochastic output Moore machine M ( λ i ) = (Mem , m 0 , α u , α n ) Synthesis in Multi-Criteria Quantitative Games M. Randour (advisors: V. Bruy` ere & J.-F. Raskin) 5 / 34

Quantitative Games Beyond Worst-Case Synthesis Multi-Dimension Objectives Window Objectives Conclusion Quantitative games on graphs Graph G = ( S , E , w ) with w : E → Z Deterministic transitions Two-player game G = ( G , S 1 , S 2 ) 2 2 � P 1 states = � P 2 states = 5 Plays have values � f : Plays( G ) → R ∪ {−∞ , ∞} − 1 7 − 4 Players follow strategies � λ i : Prefs i ( G ) → D ( S ) � Finite memory ⇒ stochastic output Moore machine M ( λ i ) = (Mem , m 0 , α u , α n ) Synthesis in Multi-Criteria Quantitative Games M. Randour (advisors: V. Bruy` ere & J.-F. Raskin) 5 / 34

Quantitative Games Beyond Worst-Case Synthesis Multi-Dimension Objectives Window Objectives Conclusion Quantitative games on graphs Graph G = ( S , E , w ) with w : E → Z Deterministic transitions Two-player game G = ( G , S 1 , S 2 ) 2 2 � P 1 states = � P 2 states = 5 Plays have values � f : Plays( G ) → R ∪ {−∞ , ∞} − 1 7 − 4 Players follow strategies � λ i : Prefs i ( G ) → D ( S ) � Finite memory ⇒ stochastic output Moore machine M ( λ i ) = (Mem , m 0 , α u , α n ) Synthesis in Multi-Criteria Quantitative Games M. Randour (advisors: V. Bruy` ere & J.-F. Raskin) 5 / 34

Quantitative Games Beyond Worst-Case Synthesis Multi-Dimension Objectives Window Objectives Conclusion Quantitative games on graphs Graph G = ( S , E , w ) with w : E → Z Deterministic transitions Two-player game G = ( G , S 1 , S 2 ) 2 2 � P 1 states = � P 2 states = 5 Plays have values � f : Plays( G ) → R ∪ {−∞ , ∞} − 1 7 − 4 Players follow strategies � λ i : Prefs i ( G ) → D ( S ) � Finite memory ⇒ stochastic output Moore machine M ( λ i ) = (Mem , m 0 , α u , α n ) Synthesis in Multi-Criteria Quantitative Games M. Randour (advisors: V. Bruy` ere & J.-F. Raskin) 5 / 34

Quantitative Games Beyond Worst-Case Synthesis Multi-Dimension Objectives Window Objectives Conclusion Quantitative games on graphs Graph G = ( S , E , w ) with w : E → Z Deterministic transitions Two-player game G = ( G , S 1 , S 2 ) 2 2 � P 1 states = � P 2 states = 5 Plays have values � f : Plays( G ) → R ∪ {−∞ , ∞} − 1 7 − 4 Players follow strategies � λ i : Prefs i ( G ) → D ( S ) � Finite memory ⇒ stochastic output Moore Then, (2 , 5 , 2) ω machine M ( λ i ) = (Mem , m 0 , α u , α n ) Synthesis in Multi-Criteria Quantitative Games M. Randour (advisors: V. Bruy` ere & J.-F. Raskin) 5 / 34

Quantitative Games Beyond Worst-Case Synthesis Multi-Dimension Objectives Window Objectives Conclusion Markov decision processes MDP P = ( G , S 1 , S ∆ , ∆) with ∆: S ∆ → D ( S ) 2 2 � P 1 states = 5 � stochastic states = MDP = game + strategy of P 2 − 1 7 � P = G [ λ 2 ] − 4 1 2 1 2 Synthesis in Multi-Criteria Quantitative Games M. Randour (advisors: V. Bruy` ere & J.-F. Raskin) 6 / 34