Semiperfect-Information Games

Abstract

Much recent research has focused on the applications of games with ω-regular objectives in the control and verification of reactive systems. However, many of the game-based models are ill-suited for these applications, because they assume that each player has complete information about the state of the system (they are “perfect-information” games). This is because in many situations, a controller does not see the private state of the plant. Such scenarios are naturally modeled by “partial-information” games. On the other hand, these games are intractable; for example, partial-information games with simple reachability objectives are 2EXPTIME-complete.

We study the intermediate case of “semiperfect-information” games, where one player has complete knowledge of the state, while the other player has only partial knowledge. This model is appropriate in control situations where a controller must cope with plant behavior that is as adversarial as possible, i.e., the controller has partial information while the plant has perfect information. As is customary, we assume that the controller and plant take turns to make moves. We show that these semiperfect-information turn-based games are equivalent to perfect-information concurrent games, where the two players choose their moves simultaneously and independently. Since the perfect-information concurrent games are well-understood, we obtain several results of how semiperfect-information turn-based games differ from perfect-information turn-based games on one hand, and from partial-information turn-based games on the other hand. In particular, semiperfect-information turn-based games can benefit from randomized strategies while the perfect-information variety cannot, and semiperfect-information turn-based games are in NP ∩ coNP for all parity objectives.