Construct and solve the safety game Sample Clauses

Construct and solve the safety game. The MDP abstraction that represents the environment and the safety automaton are transformed into a safety game. In the construction, the state space of the game is the product between the specification automaton state set and the abstraction state set. The game is played between two players. In the game, player 0 chooses the next observations from the MDP state, and player 1 chooses the next action. The safe states in the game are the ones at which the specification automaton is in a safe state and that are reachable within the abstraction. The play is won by player 1, if only safe states are visited during the play. In order to win, player 1 has to plan ahead: it can never allow the play to visit a state, from which the player 0 can force the play to visit an unsafe state in the future. This planning ahead is the true power of synthesis. Think about an autonomous car that is heading towards a cliff. It is to late, if the shield notices that something bad is happening, if the car is already falling down. The shield has to avoid all states from which avoiding the cliff is no longer possible. In the next step, the set W of winning states for player 1 is computed by standard safety game solving [12].
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