safety first a two stage algorithm for ltl games
play

Safety First: A Two-Stage Algorithm for LTL Games Saqib Sohail - PowerPoint PPT Presentation

Nov 13, 2023 •49 likes •1.28k views

Introduction Games Two Stage Synthesis Results Conclusions Safety First: A Two-Stage Algorithm for LTL Games Saqib Sohail Fabio Somenzi Department of Electrical and Computer Engineering University of Colorado at Boulder FMCAD 2009 Safety

  1. Introduction Games Two Stage Synthesis Results Conclusions Game Graphs A game graph G = (( S , E ) , S 0 , S 1 ) is a directed graph ( S , E ) with a finite state space S , a set of edges E and a partition ( S 0 , S 1 ) of the state space belonging to player 0 and 1 respectively. We assume that every state has an outgoing edge. The game is started by placing a token in one of the S init and then this token is moved along the edges, when the token is in a state s ∈ S 1 , player 1 selects one of its outgoing edges and vice-versa. The result is an infinite path in the game graph termed as a play. A strategy for a player is a recipe that specifies how to extend finite path. Formally strategy for player i is a function σ : S ∗ . S i → S . Safety First: A Two-Stage Algorithm for LTL Games

  2. Introduction Games Two Stage Synthesis Results Conclusions Parity Game For a game graph G = ( Q , E ) and a parity function π : Q → [ k ] , a parity acceptance condition requires that the maximal π ( s ) occuring infinitely often is odd (even) for player 1 ( 0 ) . A generalized parity game for a game graph G = ( Q , E ) and a set of parity functions { π i | π i : Q → [ k i ] } is played between the conjunctive and disjunctive player. The conjunctive player wins if it has a strategy to win all the parity acceptance conditions while the disjunctive player wins if it has a strategy for some parity acceptance condition. Safety First: A Two-Stage Algorithm for LTL Games

  3. Introduction Games Two Stage Synthesis Results Conclusions Parity Game For a game graph G = ( Q , E ) and a parity function π : Q → [ k ] , a parity acceptance condition requires that the maximal π ( s ) occuring infinitely often is odd (even) for player 1 ( 0 ) . A generalized parity game for a game graph G = ( Q , E ) and a set of parity functions { π i | π i : Q → [ k i ] } is played between the conjunctive and disjunctive player. The conjunctive player wins if it has a strategy to win all the parity acceptance conditions while the disjunctive player wins if it has a strategy for some parity acceptance condition. Safety First: A Two-Stage Algorithm for LTL Games

  4. Introduction Games Two Stage Synthesis Results Conclusions Two Game Theoretic Approaches The standard approach which is the focus of this talk, requires the determinization of word automata. LTL → NBW → DRW The Safraless Approach avoids determinization by working with Tree Automata. realizability lang − empt optimistic − reduction LTL → NGBW → UGCW → UGCT → NBT Safety First: A Two-Stage Algorithm for LTL Games

  5. Introduction Games Two Stage Synthesis Results Conclusions Two Game Theoretic Approaches The standard approach which is the focus of this talk, requires the determinization of word automata. LTL → NBW → DRW The Safraless Approach avoids determinization by working with Tree Automata. realizability lang − empt optimistic − reduction LTL → NGBW → UGCW → UGCT → NBT Safety First: A Two-Stage Algorithm for LTL Games

  6. Introduction Games Two Stage Synthesis Results Conclusions Specification of a simple 2-Client Arbiter Initially there are no acknowledgments. ¬ ack 0 ∧ ¬ ack 1 The acknowledgmnets are mutually exclusive. G ( ¬ ack 0 ∨ ¬ ack 1 ) There are no spurious acknowledgmnets. ∀ i . G ( ¬ req i → X ( ¬ ack i )) Every request will eventually be acknowledged ∀ i . G ( req i → F ack i ) Safety First: A Two-Stage Algorithm for LTL Games

  7. Introduction Games Two Stage Synthesis Results Conclusions Example: Game Graph and Synthesized Strategy Safety First: A Two-Stage Algorithm for LTL Games

  8. Introduction Games Two Stage Synthesis Results Conclusions Example: Game Graph and Synthesized Strategy Safety First: A Two-Stage Algorithm for LTL Games

  9. Introduction Games Two Stage Synthesis Results Conclusions Example: Game play & Strategy Computation for Player 1 � [Player 1] wins if the maximal π ( s ) occuring infinitely often is odd. Safety First: A Two-Stage Algorithm for LTL Games

  10. Introduction Games Two Stage Synthesis Results Conclusions Example: Game play & Strategy Computation for Player 1 � [Player 1] wins if the maximal π ( s ) occuring infinitely often is odd. Safety First: A Two-Stage Algorithm for LTL Games

  11. Introduction Games Two Stage Synthesis Results Conclusions Example: Game play & Strategy Computation for Player 1 � [Player 1] wins if the maximal π ( s ) occuring infinitely often is odd. Safety First: A Two-Stage Algorithm for LTL Games

  12. Introduction Games Two Stage Synthesis Results Conclusions Example: Game play & Strategy Computation for Player 1 � [Player 1] wins if the maximal π ( s ) occuring infinitely often is odd. Safety First: A Two-Stage Algorithm for LTL Games

  13. Introduction Games Two Stage Synthesis Results Conclusions Example: Game play & Strategy Computation for Player 1 � [Player 1] wins if the maximal π ( s ) occuring infinitely often is odd. Safety First: A Two-Stage Algorithm for LTL Games

  14. Introduction Games Two Stage Synthesis Results Conclusions Example: Game play & Strategy Computation for Player 1 � [Player 1] wins if the maximal π ( s ) occuring infinitely often is odd. Safety First: A Two-Stage Algorithm for LTL Games

  15. Introduction Games Two Stage Synthesis Results Conclusions Example: Game play & Strategy Computation for Player 1 � [Player 1] wins if the maximal π ( s ) occuring infinitely often is odd. Safety First: A Two-Stage Algorithm for LTL Games

  16. Introduction Games Two Stage Synthesis Results Conclusions Example: Game play & Strategy Computation for Player 1 � [Player 1] wins if the maximal π ( s ) occuring infinitely often is odd. Safety First: A Two-Stage Algorithm for LTL Games

  17. Introduction Games Two Stage Synthesis Results Conclusions Example: Game play & Strategy Computation for Player 1 � [Player 1] wins if the maximal π ( s ) occuring infinitely often is odd. Safety First: A Two-Stage Algorithm for LTL Games

  18. Introduction Games Two Stage Synthesis Results Conclusions Example: Game play & Strategy Computation for Player 1 � [Player 1] wins if the maximal π ( s ) occuring infinitely often is odd. Safety First: A Two-Stage Algorithm for LTL Games

  19. Introduction Games Two Stage Synthesis Results Conclusions Example: Game play & Strategy Computation for Player 1 � [Player 1] wins if the maximal π ( s ) occuring infinitely often is odd. Safety First: A Two-Stage Algorithm for LTL Games

  20. Introduction Games Two Stage Synthesis Results Conclusions Example: Game play & Strategy Computation for Player 1 � [Player 1] wins if the maximal π ( s ) occuring infinitely often is odd. Safety First: A Two-Stage Algorithm for LTL Games

  21. Introduction Games Two Stage Synthesis Results Conclusions Example: Game play & Strategy Computation for Player 1 � [Player 1] wins if the maximal π ( s ) occuring infinitely often is odd. Safety First: A Two-Stage Algorithm for LTL Games

  22. Introduction Games Two Stage Synthesis Results Conclusions Example: Game play & Strategy Computation for Player 1 � [Player 1] wins if the maximal π ( s ) occuring infinitely often is odd. Safety First: A Two-Stage Algorithm for LTL Games

  23. Introduction Games Two Stage Synthesis Results Conclusions Example: Game play & Strategy Computation for Player 1 � [Player 1] wins if the maximal π ( s ) occuring infinitely often is odd. Safety First: A Two-Stage Algorithm for LTL Games

  24. Introduction Games Two Stage Synthesis Results Conclusions Example: Game play & Strategy Computation for Player 1 � [Player 1] wins if the maximal π ( s ) occuring infinitely often is odd. Safety First: A Two-Stage Algorithm for LTL Games

  25. Introduction Games Two Stage Synthesis Results Conclusions Example: Game play & Strategy Computation for Player 1 � [Player 1] wins if the maximal π ( s ) occuring infinitely often is odd. Safety First: A Two-Stage Algorithm for LTL Games

  26. Introduction Games Two Stage Synthesis Results Conclusions Example: Game play & Strategy Computation for Player 1 � [Player 1] wins if the maximal π ( s ) occuring infinitely often is odd. Safety First: A Two-Stage Algorithm for LTL Games

  27. Introduction Games Two Stage Synthesis Results Conclusions Example: Game play & Strategy Computation for Player 1 � [Player 1] wins if the maximal π ( s ) occuring infinitely often is odd. Safety First: A Two-Stage Algorithm for LTL Games

  28. Introduction Games Two Stage Synthesis Results Conclusions Example: Generalized Parity Game � [Conjunctive Player] wins if it has a strategy to win all the parity functions � [Disjunctive Player] wins if it has a strategy to win according to some parity function Safety First: A Two-Stage Algorithm for LTL Games

  29. Introduction Games Two Stage Synthesis Results Conclusions Example: Generalized Parity Game � [Conjunctive Player] wins if it has a strategy to win all the parity functions � [Disjunctive Player] wins if it has a strategy to win according to some parity function Safety First: A Two-Stage Algorithm for LTL Games

  30. Introduction Games Two Stage Synthesis Results Conclusions Example: Generalized Parity Game � [Conjunctive Player] wins if it has a strategy to win all the parity functions � [Disjunctive Player] wins if it has a strategy to win according to some parity function Safety First: A Two-Stage Algorithm for LTL Games

  31. Introduction Games Two Stage Synthesis Results Conclusions Example: Generalized Parity Game � [Conjunctive Player] wins if it has a strategy to win all the parity functions � [Disjunctive Player] wins if it has a strategy to win according to some parity function Safety First: A Two-Stage Algorithm for LTL Games

  32. Introduction Games Two Stage Synthesis Results Conclusions Example: Generalized Parity Game � [Conjunctive Player] wins if it has a strategy to win all the parity functions � [Disjunctive Player] wins if it has a strategy to win according to some parity function Safety First: A Two-Stage Algorithm for LTL Games

  33. Introduction Games Two Stage Synthesis Results Conclusions Example: Generalized Parity Game � [Conjunctive Player] wins if it has a strategy to win all the parity functions � [Disjunctive Player] wins if it has a strategy to win according to some parity function Safety First: A Two-Stage Algorithm for LTL Games

  34. Introduction Games Two Stage Synthesis Results Conclusions Example: Generalized Parity Game � [Conjunctive Player] wins if it has a strategy to win all the parity functions � [Disjunctive Player] wins if it has a strategy to win according to some parity function Safety First: A Two-Stage Algorithm for LTL Games

  35. Introduction Games Two Stage Synthesis Results Conclusions Example: Generalized Parity Game � [Conjunctive Player] wins if it has a strategy to win all the parity functions � [Disjunctive Player] wins if it has a strategy to win according to some parity function Safety First: A Two-Stage Algorithm for LTL Games

  36. Introduction Games Two Stage Synthesis Results Conclusions Example: Generalized Parity Game � [Conjunctive Player] wins if it has a strategy to win all the parity functions � [Disjunctive Player] wins if it has a strategy to win according to some parity function Safety First: A Two-Stage Algorithm for LTL Games

  37. Introduction The Challenge Games Algorithm Two Stage Synthesis Optimizations Results Implementation Conclusions Caveats Outline 1 Introduction 2 Games 3 Two Stage Synthesis The Challenge Algorithm Optimizations Implementation Caveats 4 Results 5 Conclusions Safety First: A Two-Stage Algorithm for LTL Games

  38. Introduction The Challenge Games Algorithm Two Stage Synthesis Optimizations Results Implementation Conclusions Caveats The Challenge Generalized parity game is an NP-Complete problem and the current algorithm (Chatterjee et. al 07) is computationally very expensive. Is there a simpler solution to the complex problem? Is there a way to deal with properties one at a time? Safety First: A Two-Stage Algorithm for LTL Games

  39. Introduction The Challenge Games Algorithm Two Stage Synthesis Optimizations Results Implementation Conclusions Caveats The Challenge Generalized parity game is an NP-Complete problem and the current algorithm (Chatterjee et. al 07) is computationally very expensive. Is there a simpler solution to the complex problem? Is there a way to deal with properties one at a time? Safety First: A Two-Stage Algorithm for LTL Games

  40. Introduction The Challenge Games Algorithm Two Stage Synthesis Optimizations Results Implementation Conclusions Caveats The Challenge Generalized parity game is an NP-Complete problem and the current algorithm (Chatterjee et. al 07) is computationally very expensive. Is there a simpler solution to the complex problem? Is there a way to deal with properties one at a time? Safety First: A Two-Stage Algorithm for LTL Games

  41. Introduction The Challenge Games Algorithm Two Stage Synthesis Optimizations Results Implementation Conclusions Caveats Safety Properties A safety condition for a game graph G = ( Q , E ) is a function π : Q → { 0 , 1 } such that there is no transition ( u , v ) ∈ E such that π ( u ) = 0 and π ( v ) = 1. Safety First: A Two-Stage Algorithm for LTL Games

  42. Introduction The Challenge Games Algorithm Two Stage Synthesis Optimizations Results Implementation Conclusions Caveats Safety Properties A safety condition for a game graph G = ( Q , E ) is a function π : Q → { 0 , 1 } such that there is no transition ( u , v ) ∈ E such that π ( u ) = 0 and π ( v ) = 1. Safety First: A Two-Stage Algorithm for LTL Games

  43. Introduction The Challenge Games Algorithm Two Stage Synthesis Optimizations Results Implementation Conclusions Caveats Persistence Properties A persistence condition for a game graph G = ( Q , E ) is a function π : Q → { 1 , 2 } . Safety First: A Two-Stage Algorithm for LTL Games

  44. Introduction The Challenge Games Algorithm Two Stage Synthesis Optimizations Results Implementation Conclusions Caveats The Claim What is so unique about persistence properties? The winning states for persistence properties can be categorized into persistent and transient states. The computation of strategies is not necessary when we are only interested in determining the persistent and transient states. A transient state will stay a transient state for the subsequent games. Safety First: A Two-Stage Algorithm for LTL Games

  45. Introduction The Challenge Games Algorithm Two Stage Synthesis Optimizations Results Implementation Conclusions Caveats The Claim What is so unique about persistence properties? The winning states for persistence properties can be categorized into persistent and transient states. The computation of strategies is not necessary when we are only interested in determining the persistent and transient states. A transient state will stay a transient state for the subsequent games. Safety First: A Two-Stage Algorithm for LTL Games

  46. Introduction The Challenge Games Algorithm Two Stage Synthesis Optimizations Results Implementation Conclusions Caveats The Claim What is so unique about persistence properties? The winning states for persistence properties can be categorized into persistent and transient states. The computation of strategies is not necessary when we are only interested in determining the persistent and transient states. A transient state will stay a transient state for the subsequent games. Safety First: A Two-Stage Algorithm for LTL Games

  47. Introduction The Challenge Games Algorithm Two Stage Synthesis Optimizations Results Implementation Conclusions Caveats The Claim What is so unique about persistence properties? The winning states for persistence properties can be categorized into persistent and transient states. The computation of strategies is not necessary when we are only interested in determining the persistent and transient states. A transient state will stay a transient state for the subsequent games. Safety First: A Two-Stage Algorithm for LTL Games

  48. Introduction The Challenge Games Algorithm Two Stage Synthesis Optimizations Results Implementation Conclusions Caveats Input/Output based game → State based game Safety First: A Two-Stage Algorithm for LTL Games

  49. Introduction The Challenge Games Algorithm Two Stage Synthesis Optimizations Results Implementation Conclusions Caveats Example: Simple Arbiter revisited Safety First: A Two-Stage Algorithm for LTL Games

  50. Introduction The Challenge Games Algorithm Two Stage Synthesis Optimizations Results Implementation Conclusions Caveats Example: Simple Arbiter revisited Safety First: A Two-Stage Algorithm for LTL Games

  51. Introduction The Challenge Games Algorithm Two Stage Synthesis Optimizations Results Implementation Conclusions Caveats Example: Simple Arbiter revisited Safety First: A Two-Stage Algorithm for LTL Games

  52. Introduction The Challenge Games Algorithm Two Stage Synthesis Optimizations Results Implementation Conclusions Caveats Example: Simple Arbiter revisited Safety First: A Two-Stage Algorithm for LTL Games

  53. Introduction The Challenge Games Algorithm Two Stage Synthesis Optimizations Results Implementation Conclusions Caveats Example: Simple Arbiter revisited Safety First: A Two-Stage Algorithm for LTL Games

  54. Introduction The Challenge Games Algorithm Two Stage Synthesis Optimizations Results Implementation Conclusions Caveats Example: Simple Arbiter revisited Safety First: A Two-Stage Algorithm for LTL Games

  55. Introduction The Challenge Games Algorithm Two Stage Synthesis Optimizations Results Implementation Conclusions Caveats Example: Simple Arbiter revisited Safety First: A Two-Stage Algorithm for LTL Games

  56. Introduction The Challenge Games Algorithm Two Stage Synthesis Optimizations Results Implementation Conclusions Caveats Example: Simple Arbiter revisited Safety First: A Two-Stage Algorithm for LTL Games

  57. Introduction The Challenge Games Algorithm Two Stage Synthesis Optimizations Results Implementation Conclusions Caveats Example: Simple Arbiter revisited Safety First: A Two-Stage Algorithm for LTL Games

  58. Introduction The Challenge Games Algorithm Two Stage Synthesis Optimizations Results Implementation Conclusions Caveats Example: Simple Arbiter revisited Safety First: A Two-Stage Algorithm for LTL Games

  59. Introduction The Challenge Games Algorithm Two Stage Synthesis Optimizations Results Implementation Conclusions Caveats Example: Simple Arbiter revisited Safety First: A Two-Stage Algorithm for LTL Games

  60. Introduction The Challenge Games Algorithm Two Stage Synthesis Optimizations Results Implementation Conclusions Caveats Example: Simple Arbiter revisited Safety First: A Two-Stage Algorithm for LTL Games

  61. Introduction The Challenge Games Algorithm Two Stage Synthesis Optimizations Results Implementation Conclusions Caveats Example: Simple Arbiter revisited Safety First: A Two-Stage Algorithm for LTL Games

  62. Introduction The Challenge Games Algorithm Two Stage Synthesis Optimizations Results Implementation Conclusions Caveats Example: Simple Arbiter revisited Safety First: A Two-Stage Algorithm for LTL Games

  63. Introduction The Challenge Games Algorithm Two Stage Synthesis Optimizations Results Implementation Conclusions Caveats Example: Simple Arbiter revisited Safety First: A Two-Stage Algorithm for LTL Games

  64. Introduction The Challenge Games Algorithm Two Stage Synthesis Optimizations Results Implementation Conclusions Caveats Example: Simple Arbiter revisited Safety First: A Two-Stage Algorithm for LTL Games

  65. Introduction The Challenge Games Algorithm Two Stage Synthesis Optimizations Results Implementation Conclusions Caveats Example: Simple Arbiter revisited Safety First: A Two-Stage Algorithm for LTL Games

  66. Introduction The Challenge Games Algorithm Two Stage Synthesis Optimizations Results Implementation Conclusions Caveats Example: Simple Arbiter revisited Safety First: A Two-Stage Algorithm for LTL Games

  67. Introduction The Challenge Games Algorithm Two Stage Synthesis Optimizations Results Implementation Conclusions Caveats How significant is the improvement? The complexity of “classical” algorithm of (Chatterjee et al 07) is given by � � d O ( m · n 2 d ) · , d 1 , d 2 , . . . , d k d i = ⌈ k i / 2 ⌉ If π k is a safety condition, solving the game in two stages leads d − 1 to a better bound for the second stage, O ( m · n 2 d − 2 ) · � � , d 1 ,..., d k − 1 while the first stage runs in O ( m · n 2 ) . In practice, in the second stage, the number of transitions may decrease, and the removal of losing positions for π 1 may reduce the number of colors in the remaining conditions. Safety First: A Two-Stage Algorithm for LTL Games

  68. Introduction The Challenge Games Algorithm Two Stage Synthesis Optimizations Results Implementation Conclusions Caveats How significant is the improvement? The complexity of “classical” algorithm of (Chatterjee et al 07) is given by � � d O ( m · n 2 d ) · , d 1 , d 2 , . . . , d k d i = ⌈ k i / 2 ⌉ If π k is a safety condition, solving the game in two stages leads d − 1 to a better bound for the second stage, O ( m · n 2 d − 2 ) · � � , d 1 ,..., d k − 1 while the first stage runs in O ( m · n 2 ) . In practice, in the second stage, the number of transitions may decrease, and the removal of losing positions for π 1 may reduce the number of colors in the remaining conditions. Safety First: A Two-Stage Algorithm for LTL Games

  69. Introduction The Challenge Games Algorithm Two Stage Synthesis Optimizations Results Implementation Conclusions Caveats Outline 1 Introduction 2 Games 3 Two Stage Synthesis The Challenge Algorithm Optimizations Implementation Caveats 4 Results 5 Conclusions Safety First: A Two-Stage Algorithm for LTL Games

  70. Introduction The Challenge Games Algorithm Two Stage Synthesis Optimizations Results Implementation Conclusions Caveats Methodology Identify the safety/persistent properties in the specification. Translate each property into a deterministic automaton. Compose the automaton with already existing game-graph and then playing the 2-player game on the relevant section of the graph. Determinize all the remaining non-safety/non-persistent properties and then compose with the game-graph and play the final generalized parity game on the relevant section of the graph. Select an appropriate strategy which in conjunction with the property automata can be translated into software/hardware. Safety First: A Two-Stage Algorithm for LTL Games

  71. Introduction The Challenge Games Algorithm Two Stage Synthesis Optimizations Results Implementation Conclusions Caveats Methodology Identify the safety/persistent properties in the specification. Translate each property into a deterministic automaton. Compose the automaton with already existing game-graph and then playing the 2-player game on the relevant section of the graph. Determinize all the remaining non-safety/non-persistent properties and then compose with the game-graph and play the final generalized parity game on the relevant section of the graph. Select an appropriate strategy which in conjunction with the property automata can be translated into software/hardware. Safety First: A Two-Stage Algorithm for LTL Games

  72. Introduction The Challenge Games Algorithm Two Stage Synthesis Optimizations Results Implementation Conclusions Caveats Methodology Identify the safety/persistent properties in the specification. Translate each property into a deterministic automaton. Compose the automaton with already existing game-graph and then playing the 2-player game on the relevant section of the graph. Determinize all the remaining non-safety/non-persistent properties and then compose with the game-graph and play the final generalized parity game on the relevant section of the graph. Select an appropriate strategy which in conjunction with the property automata can be translated into software/hardware. Safety First: A Two-Stage Algorithm for LTL Games

  73. Introduction The Challenge Games Algorithm Two Stage Synthesis Optimizations Results Implementation Conclusions Caveats Methodology Identify the safety/persistent properties in the specification. Translate each property into a deterministic automaton. Compose the automaton with already existing game-graph and then playing the 2-player game on the relevant section of the graph. Determinize all the remaining non-safety/non-persistent properties and then compose with the game-graph and play the final generalized parity game on the relevant section of the graph. Select an appropriate strategy which in conjunction with the property automata can be translated into software/hardware. Safety First: A Two-Stage Algorithm for LTL Games

  74. Introduction The Challenge Games Algorithm Two Stage Synthesis Optimizations Results Implementation Conclusions Caveats Methodology Identify the safety/persistent properties in the specification. Translate each property into a deterministic automaton. Compose the automaton with already existing game-graph and then playing the 2-player game on the relevant section of the graph. Determinize all the remaining non-safety/non-persistent properties and then compose with the game-graph and play the final generalized parity game on the relevant section of the graph. Select an appropriate strategy which in conjunction with the property automata can be translated into software/hardware. Safety First: A Two-Stage Algorithm for LTL Games

  75. Introduction The Challenge Games Algorithm Two Stage Synthesis Optimizations Results Implementation Conclusions Caveats Algorithm S AFETY -F IRST ( G , SPECIFICATION ) 1. ( SAFETY , NON − PERSISTENT ) ← SPECIFICATION 2. 3. foreach ϕ ∈ SAFETY 3.1 G = G � automaton ϕ det 3.2 ( Q sys , E sys ) ← C HATTERJEE ( G , ϕ ) 3.3 ( Q new , E new ) ← O PTIMIZE ( Q sys , E sys ) 3.4 G = ( Q new , E new ) end foreach foreach ϕ ∈ NON − PERSISTENT 4. 4.1 G = G � automaton ϕ det end foreach ( Q sys , E sys , σ sys ) ← C HATTERJEE ( G , ϕ 1 , ϕ 2 ..., ϕ n ) 5 S YNTHESIZE ( Q sys , E sys , σ sys ) 6 Safety First: A Two-Stage Algorithm for LTL Games

  76. Introduction The Challenge Games Algorithm Two Stage Synthesis Optimizations Results Implementation Conclusions Caveats Algorithm S AFETY -F IRST ( G , SPECIFICATION ) 1. ( SAFETY , NON − PERSISTENT ) ← SPECIFICATION 2. 3. foreach ϕ ∈ SAFETY 3.1 G = G � automaton ϕ det 3.2 ( Q sys , E sys ) ← C HATTERJEE ( G , ϕ ) 3.3 ( Q new , E new ) ← O PTIMIZE ( Q sys , E sys ) 3.4 G = ( Q new , E new ) end foreach foreach ϕ ∈ NON − PERSISTENT 4. 4.1 G = G � automaton ϕ det end foreach ( Q sys , E sys , σ sys ) ← C HATTERJEE ( G , ϕ 1 , ϕ 2 ..., ϕ n ) 5 S YNTHESIZE ( Q sys , E sys , σ sys ) 6 Safety First: A Two-Stage Algorithm for LTL Games

  77. Introduction The Challenge Games Algorithm Two Stage Synthesis Optimizations Results Implementation Conclusions Caveats Algorithm S AFETY -F IRST ( G , SPECIFICATION ) 1. ( SAFETY , NON − PERSISTENT ) ← SPECIFICATION 2. 3. foreach ϕ ∈ SAFETY 3.1 G = G � automaton ϕ det 3.2 ( Q sys , E sys ) ← C HATTERJEE ( G , ϕ ) 3.3 ( Q new , E new ) ← O PTIMIZE ( Q sys , E sys ) 3.4 G = ( Q new , E new ) end foreach foreach ϕ ∈ NON − PERSISTENT 4. 4.1 G = G � automaton ϕ det end foreach ( Q sys , E sys , σ sys ) ← C HATTERJEE ( G , ϕ 1 , ϕ 2 ..., ϕ n ) 5 S YNTHESIZE ( Q sys , E sys , σ sys ) 6 Safety First: A Two-Stage Algorithm for LTL Games

  78. Introduction The Challenge Games Algorithm Two Stage Synthesis Optimizations Results Implementation Conclusions Caveats Algorithm S AFETY -F IRST ( G , SPECIFICATION ) 1. ( SAFETY , NON − PERSISTENT ) ← SPECIFICATION 2. 3. foreach ϕ ∈ SAFETY 3.1 G = G � automaton ϕ det 3.2 ( Q sys , E sys ) ← C HATTERJEE ( G , ϕ ) 3.3 ( Q new , E new ) ← O PTIMIZE ( Q sys , E sys ) 3.4 G = ( Q new , E new ) end foreach foreach ϕ ∈ NON − PERSISTENT 4. 4.1 G = G � automaton ϕ det end foreach ( Q sys , E sys , σ sys ) ← C HATTERJEE ( G , ϕ 1 , ϕ 2 ..., ϕ n ) 5 S YNTHESIZE ( Q sys , E sys , σ sys ) 6 Safety First: A Two-Stage Algorithm for LTL Games

  79. Introduction The Challenge Games Algorithm Two Stage Synthesis Optimizations Results Implementation Conclusions Caveats Algorithm S AFETY -F IRST ( G , SPECIFICATION ) 1. ( SAFETY , NON − PERSISTENT ) ← SPECIFICATION 2. 3. foreach ϕ ∈ SAFETY 3.1 G = G � automaton ϕ det 3.2 ( Q sys , E sys ) ← C HATTERJEE ( G , ϕ ) 3.3 ( Q new , E new ) ← O PTIMIZE ( Q sys , E sys ) 3.4 G = ( Q new , E new ) end foreach foreach ϕ ∈ NON − PERSISTENT 4. 4.1 G = G � automaton ϕ det end foreach ( Q sys , E sys , σ sys ) ← C HATTERJEE ( G , ϕ 1 , ϕ 2 ..., ϕ n ) 5 S YNTHESIZE ( Q sys , E sys , σ sys ) 6 Safety First: A Two-Stage Algorithm for LTL Games

  80. Introduction The Challenge Games Algorithm Two Stage Synthesis Optimizations Results Implementation Conclusions Caveats Algorithm S AFETY -F IRST ( G , SPECIFICATION ) 1. ( SAFETY , NON − PERSISTENT ) ← SPECIFICATION 2. 3. foreach ϕ ∈ SAFETY 3.1 G = G � automaton ϕ det 3.2 ( Q sys , E sys ) ← C HATTERJEE ( G , ϕ ) 3.3 ( Q new , E new ) ← O PTIMIZE ( Q sys , E sys ) 3.4 G = ( Q new , E new ) end foreach foreach ϕ ∈ NON − PERSISTENT 4. 4.1 G = G � automaton ϕ det end foreach ( Q sys , E sys , σ sys ) ← C HATTERJEE ( G , ϕ 1 , ϕ 2 ..., ϕ n ) 5 S YNTHESIZE ( Q sys , E sys , σ sys ) 6 Safety First: A Two-Stage Algorithm for LTL Games

  81. Introduction The Challenge Games Algorithm Two Stage Synthesis Optimizations Results Implementation Conclusions Caveats Outline 1 Introduction 2 Games 3 Two Stage Synthesis The Challenge Algorithm Optimizations Implementation Caveats 4 Results 5 Conclusions Safety First: A Two-Stage Algorithm for LTL Games

  82. Introduction The Challenge Games Algorithm Two Stage Synthesis Optimizations Results Implementation Conclusions Caveats Restrict the state space with the reachable winning states. Remove the constant bits in the reachable winning state space. Find dependencies between state-variables and remove the dependant variables. (Efficiently re-encode the state space). Safety First: A Two-Stage Algorithm for LTL Games

  83. Introduction The Challenge Games Algorithm Two Stage Synthesis Optimizations Results Implementation Conclusions Caveats Restrict the state space with the reachable winning states. Remove the constant bits in the reachable winning state space. Find dependencies between state-variables and remove the dependant variables. (Efficiently re-encode the state space). Safety First: A Two-Stage Algorithm for LTL Games

  84. Introduction The Challenge Games Algorithm Two Stage Synthesis Optimizations Results Implementation Conclusions Caveats Restrict the state space with the reachable winning states. Remove the constant bits in the reachable winning state space. Find dependencies between state-variables and remove the dependant variables. (Efficiently re-encode the state space). Safety First: A Two-Stage Algorithm for LTL Games

Download Presentation
Download Policy: The content available on the website is offered to you 'AS IS' for your personal information and use only. It cannot be commercialized, licensed, or distributed on other websites without prior consent from the author. To download a presentation, simply click this link. If you encounter any difficulties during the download process, it's possible that the publisher has removed the file from their server.

Recommend

Strategic Commitment in Two-Stage Games (Mathematical Version) General Theory Stage 1: Player 1

Strategic Commitment in Two-Stage Games (Mathematical Version) General Theory Stage 1: Player 1

ECO 305 Microeconomic Theory Strategic Commitment in Two-Stage Games (Mathematical Version) General Theory Stage 1: Player 1 chooses K , Investment Stage 2: Players 1, 2 choose actions x 1 , x 2 . Payoffs F 1 ( x 1 , x 2 , K ), F 2 ( x

207 views • 4 slides
Evolving Technique An Algorithm for 1-Stage Versus 2-Stage Exchange: Here are the Rules Michael

Evolving Technique An Algorithm for 1-Stage Versus 2-Stage Exchange: Here are the Rules Michael

ADULT RECONSTRUCTION AND JOINT REPLACEMENT Evolving Technique An Algorithm for 1-Stage Versus 2-Stage Exchange: Here are the Rules Michael B. Cross, MD Assistant Attending Orthopaedic Surgeon Disclosures Consultant: Smith &

322 views • 17 slides
Using Video Games for Workplace Safety Training Pennsylvania Governors Occupational Safety and

Using Video Games for Workplace Safety Training Pennsylvania Governors Occupational Safety and

Using Video Games for Workplace Safety Training Pennsylvania Governors Occupational Safety and Health Conference, October 2018 Ken Smith, Simcoach Games How I came to believe in using Video Games 25 year career in workforce management

974 views • 8 slides
A Simple Algorithm for Solving Qualitative Probabilistic Parity Games Sven Schewe University of

A Simple Algorithm for Solving Qualitative Probabilistic Parity Games Sven Schewe University of

A Simple Algorithm for Solving Qualitative Probabilistic Parity Games Sven Schewe University of Liverpool joint work with Ernst Moritz Hahn, Andrea Turrini & Lijun Zhang motivation reachability games & attractors parity games

486 views • 29 slides
Repeated Games with Perfect Monitoring Mihai Manea MIT Repeated Games normal-form stage game

Repeated Games with Perfect Monitoring Mihai Manea MIT Repeated Games normal-form stage game

Repeated Games with Perfect Monitoring Mihai Manea MIT Repeated Games normal-form stage game G = ( N , A , u ) players simultaneously play game G at time t = 0 , 1 , . . . at each date t , players observe all past actions: h t = ( a 0

163 views • 14 slides
ITERATION ALGORITHM TO CREATE FRACTALS UNIVERSITY OF MARYLAND DIRECTED READING PROGRAM FALL 2015

ITERATION ALGORITHM TO CREATE FRACTALS UNIVERSITY OF MARYLAND DIRECTED READING PROGRAM FALL 2015

USING THE RANDOM ITERATION ALGORITHM TO CREATE FRACTALS UNIVERSITY OF MARYLAND DIRECTED READING PROGRAM FALL 2015 BY ADAM ANDERSON THE SIERPINSKI GASKET 2 Stage 1: Stage 0: Stage 2: Stage n: 2 2 2 1 3 1 2 A 0 = 2 3 3 2 A n

461 views • 29 slides
Parity to Safety in Polynomial Time for Pushdown and Collapsible Pushdown Games Matthew Hague

Parity to Safety in Polynomial Time for Pushdown and Collapsible Pushdown Games Matthew Hague

Parity to Safety in Polynomial Time for Pushdown and Collapsible Pushdown Games Matthew Hague Royal Holloway, University of London with Roland Meyer, Sebastian Muskalla,and Martin Zimmermann Abstract Safety games for pushdown systems:

890 views • 71 slides
A Unified Distributed Algorithm for Non- Games Non-cooperative, Non-convex, and Non-differentiable

A Unified Distributed Algorithm for Non- Games Non-cooperative, Non-convex, and Non-differentiable

A Unified Distributed Algorithm for Non- Games Non-cooperative, Non-convex, and Non-differentiable Jong-Shi Pang and Meisam Razaviyayn presented at Workshop on Optimization for Modern Computation Peking University, Beijing, China 10:10

658 views • 20 slides
Safety at sea TRINITY HOUSE // KEY STAGE 3 SAFETY AT SEA Starter Activity 1 TRINITY

Safety at sea TRINITY HOUSE // KEY STAGE 3 SAFETY AT SEA Starter Activity 1 TRINITY

Safety at sea TRINITY HOUSE // KEY STAGE 3 SAFETY AT SEA Starter Activity 1 TRINITY HOUSE // KEY STAGE 3 SAFETY AT SEA Starter What am I? TRINITY HOUSE // KEY STAGE 3 SAFETY AT SEA What am I? I am usually painted in I communicate

501 views • 23 slides
Fun and Games with Graphs CS200 - Graphs 1 8 7 7 5 9 S 5 15 6 8 9 11 Do Dijkstras

Fun and Games with Graphs CS200 - Graphs 1 8 7 7 5 9 S 5 15 6 8 9 11 Do Dijkstras

Fun and Games with Graphs CS200 - Graphs 1 8 7 7 5 9 S 5 15 6 8 9 11 Do Dijkstras Shortest Paths Algorithm, Source: S CS200 - Class Overview 2 8 7 7 5 9 S 5 15 6 8 9 11 Do Prims Minimum Spanning Tree Algorithm,

368 views • 26 slides
Single-Deviation Principle and Bargaining Mihai Manea MIT Multi-stage games with observable

Single-Deviation Principle and Bargaining Mihai Manea MIT Multi-stage games with observable

Single-Deviation Principle and Bargaining Mihai Manea MIT Multi-stage games with observable actions finite set of players N stages t = 0 , 1 , 2 , . . . H : set of terminal histories (sequences of action profiles of possibly

415 views • 24 slides
4 Heuristic Search 4.0 Introduction 4.3 Using Heuristics in Games 4.1 An Algorithm for

4 Heuristic Search 4.0 Introduction 4.3 Using Heuristics in Games 4.1 An Algorithm for

4 Heuristic Search 4.0 Introduction 4.3 Using Heuristics in Games 4.1 An Algorithm for Heuristic Search 4.4 Complexity Issues 4.2 Admissibility, 4.5 Epilogue and Monotonicity, and References Informedness 4.6 Exercises Additional

536 views • 53 slides
4 Heuristic Search 4.0 Introduction 4.3 Using Heuristics in Games 4.1 An Algorithm for

4 Heuristic Search 4.0 Introduction 4.3 Using Heuristics in Games 4.1 An Algorithm for

4 Heuristic Search 4.0 Introduction 4.3 Using Heuristics in Games 4.1 An Algorithm for Heuristic Search 4.4 Complexity Issues 4.2 Admissibility, 4.5 Epilogue and Monotonicity, and References Informedness 4.6 Exercises Additional

1.04k views • 78 slides
Operator approach to stochastic games with varying stage duration G.Vigeral (with S. Sorin)

Operator approach to stochastic games with varying stage duration G.Vigeral (with S. Sorin)

Operator approach to stochastic games with varying stage duration G.Vigeral (with S. Sorin) CEREMADE Universite Paris Dauphine 26 January 2016, ADGO II, Santiago de Chile 1 G.Vigeral (with S. Sorin) Operator approach Table of contents

548 views • 32 slides
Down the Borel Hierarchy: Solving Muller Games via Safety Games Joint work with Daniel Neider and

Down the Borel Hierarchy: Solving Muller Games via Safety Games Joint work with Daniel Neider and

Down the Borel Hierarchy: Solving Muller Games via Safety Games Joint work with Daniel Neider and Roman Rabinovich (RWTH Aachen University) Martin Zimmermann University of Warsaw June 25th, 2012 LICS 2012 Dubrovnik, Croatia Martin Zimmermann

419 views • 13 slides
A Discrete Strategy Improvement Algorithm for Solving Parity Games Jens V oge Marcin

A Discrete Strategy Improvement Algorithm for Solving Parity Games Jens V oge Marcin

A Discrete Strategy Improvement Algorithm for Solving Parity Games Jens V oge Marcin Jurdzi nski Lehrstuhl f ur Informatik VII BRICS RWTH Aachen University of Aarhus Germany Denmark Chicago, USA, 19 July 2000 1 Complexity of

295 views • 11 slides
Persistent currents in two dimension: New regimes induced by the interplay between electronic

Persistent currents in two dimension: New regimes induced by the interplay between electronic

Persistent currents in two dimension: New regimes induced by the interplay between electronic correlations and disorder Zoltn dm Nmeth Jean-Louis Pichard CEA - Saclay, Service de Physique de l'Etat Condens Outline: Overview of

583 views • 30 slides
Dynamic Partial-Order Reduction for Model Checking Software Cormac Flanagan Patrice Godefroid

Dynamic Partial-Order Reduction for Model Checking Software Cormac Flanagan Patrice Godefroid

Dynamic Partial-Order Reduction for Model Checking Software Cormac Flanagan Patrice Godefroid UC Santa Cruz Bell Labs Presented by: Ulrich Mller Model Checking Given a multithreaded program Wed like to check for deadlocks and

462 views • 17 slides
Ohios Health Home Model for Beneficiaries with Serious and Persistent Mental Illness: A

Ohios Health Home Model for Beneficiaries with Serious and Persistent Mental Illness: A

Exploring Medicaid Health Homes: Ohios Health Home Model for Beneficiaries with Serious and Persistent Mental Illness: A Regional Roll-Out November 5, 2012; 3:00 4:00PM (ET) For audio, dial: 1-800-273-7043; Passcode: 596413 A video

350 views • 9 slides
MillWheel: Fault Tolerant Stream Processing at Internet Scale Presented by Rui Zhang October

MillWheel: Fault Tolerant Stream Processing at Internet Scale Presented by Rui Zhang October

MillWheel: Fault Tolerant Stream Processing at Internet Scale Presented by Rui Zhang October 28, 2013 What is MillWheel? Stream processing framework Simple programming models User specified directed computation graph Fault

670 views • 27 slides
Disclosures Nothing to disclose ABSTRACT PROFFERED TALK: Large ( 2 cm) Breast Cancers in

Disclosures Nothing to disclose ABSTRACT PROFFERED TALK: Large ( 2 cm) Breast Cancers in

6/9/2017 Disclosures Nothing to disclose ABSTRACT PROFFERED TALK: Large ( 2 cm) Breast Cancers in Women Attending Regular Screening: Risk Factors and Implications for Prognosis FREDRIK STRAND, MD, MSc, PhD Cand. Karolinska Stockholm,

287 views • 5 slides
Approximation and Non-parametric Estimation of ResNet-type Convolutional Neural Networks Kenta

Approximation and Non-parametric Estimation of ResNet-type Convolutional Neural Networks Kenta

Poster: 13 th June, Pacific Ballroom #77 Paper Link Approximation and Non-parametric Estimation of ResNet-type Convolutional Neural Networks Kenta Oono 1,2 Taiji Suzuki 1,3 {kenta_oono, taiji}@mist.i.u-tokyo.ac.jp 1. The University of Tokyo

1.26k views • 23 slides
Installation and Integration Meeting Bi-Weekly Update EOI information and Installation Reviews

Installation and Integration Meeting Bi-Weekly Update EOI information and Installation Reviews

Installation and Integration Meeting Bi-Weekly Update EOI information and Installation Reviews William Miller University of Minnesota Feb . 24 th , 2016 v2 Ash River-Trail Assembly Design Meeting Feb 15 th with Jack Fowler (Duke), Dan

98 views • 8 slides
1 Quick recap of EM negative total-data log-likelihood free energy likelihood p

1 Quick recap of EM negative total-data log-likelihood free energy likelihood p

Statistical Modeling and Analysis of Neural Data (NEU 560) Princeton University, Spring 2018 Jonathan Pillow Lecture 17 notes: Latent variable models and EM Thurs, 4.12 1 Quick recap of EM negative total-data log-likelihood free energy

459 views • 5 slides

More recommend