de Alfaro, Luca ; Henzinger, Thomas AIST Austria ; Kupferman, Orna
An open system can be modeled as a two-player game between the system and its environment. At each round of the game, player 1 (the system) and player 2 (the environment) independently and simultaneously choose moves, and the two choices determine the next state of the game. Properties of open systems can be modeled as objectives of these two-player games. For the basic objective of reachability-can player 1 force the game to a given set of target states?-there are three types of winning states, according to the degree of certainty with which player 1 can reach the target. From type-1 states, player 1 has a deterministic strategy to always reach the target. From type-2 states, player 1 has a randomized strategy to reach the target with probability 1. From type-3 states, player 1 has for every real ε>0 a randomized strategy to reach the target with probability greater than 1-ε. We show that for finite state spaces, all three sets of winning states can be computed in polynomial time: type-1 states in linear time, and type-2 and type-3 states in quadratic time. The algorithms to compute the three sets of winning states also enable the construction of the winning and spoiling strategies. Finally, we apply our results by introducing a temporal logic in which all three kinds of winning conditions can be specified, and which can be model checked in polynomial time. This logic, called Randomized ATL, is suitable for reasoning about randomized behavior in open (two-agent) as well as multi-agent systems
564 - 575
FOCS: Foundations of Computer Science
De Alfaro L, Henzinger TA, Kupferman O. Concurrent reachability games. In: IEEE; 1998:564-575. doi:10.1109/SFCS.1998.743507
De Alfaro, L., Henzinger, T. A., & Kupferman, O. (1998). Concurrent reachability games (pp. 564–575). Presented at the FOCS: Foundations of Computer Science, IEEE. https://doi.org/10.1109/SFCS.1998.743507
De Alfaro, Luca, Thomas A Henzinger, and Orna Kupferman. “Concurrent Reachability Games,” 564–75. IEEE, 1998. https://doi.org/10.1109/SFCS.1998.743507 .
L. De Alfaro, T. A. Henzinger, and O. Kupferman, “Concurrent reachability games,” presented at the FOCS: Foundations of Computer Science, 1998, pp. 564–575.
De Alfaro L, Henzinger TA, Kupferman O. 1998. Concurrent reachability games. FOCS: Foundations of Computer Science 564–575.
De Alfaro, Luca, et al. Concurrent Reachability Games. IEEE, 1998, pp. 564–75, doi:10.1109/SFCS.1998.743507 .