In distributed synthesis, we generate a set of process implementations that, together, accomplish an objective against all possible behaviors of the environment. A lot of recent work has focussed on systems with causal memory, i.e., sets of asynchronous processes that exchange their causal histories upon synchronization. Decidability results for this problem have been stated either in terms of control games, which extend Zielonka's asynchronous automata by partitioning the actions into controllable and uncontrollable, or in terms of Petri games, which extend Petri nets by partitioning the tokens into system and environment players. The precise connection between these two models was so far, however, an open question. In this paper, we provide the first formal connection between control games and Petri games. We establish the equivalence of the two game models based on weak bisimulations between their strategies. For both directions, we show that a game of one type can be translated into an equivalent game of the other type. We provide exponential upper and lower bounds for the translations. Our translations make it possible to transfer and combine decidability results between the two types of games. Exemplarily, we translate decidability in acyclic communication architectures, originally obtained for control games, to Petri games, and decidability in single-process systems, originally obtained for Petri games, to control games.
For control games, there are non-elementary decidability results for restrictions on the dependencies of actions @cite_0 and for acyclic communication architectures @cite_18 @cite_4 . Decidability of process-based control games has also been obtained for restrictions on the synchronization behavior @cite_9 @cite_21 . Recently, results on control games have been unified and extended by a new proof technique for the class of decomposable games @cite_6 .
@cite_18 @cite_4 @cite_9 @cite_21 @cite_6 @cite_0
2610229352 2103151730 2401523698 2810102121
The decidability of the distributed version of the Ramadge and Wonham controller synthesis problem, where both the plant and the controllers are modeled as asynchronous automata and the controllers have causal memory is a challenging open problem. There exist three classes of plants for which the existence of a correct controller with causal memory has been shown decidable: when the dependency graph of actions is series-parallel, when the processes are connectedly communicating and when the dependency graph of processes is a tree. We design a class of plants, called decomposable games, with a decidable controller synthesis problem. This provides a unified proof of the three existing decidability results as well as new examples of decidable plants. We present a view of cooperative control using the language of learning in games. We review the game-theoretic concepts of potential and weakly acyclic games, and demonstrate how several cooperative control problems, such as consensus and dynamic sensor coverage, can be formulated in these settings. Motivated by this connection, we build upon game-theoretic concepts to better accommodate a broader class of cooperative control problems. In particular, we extend existing learning algorithms to accommodate restricted action sets caused by the limitations of agent capabilities and group based decision making. Furthermore, we also introduce a new class of games called sometimes weakly acyclic games for time-varying objective functions and action sets, and provide distributed algorithms for convergence to an equilibrium. The Atari 2600 games supported in the Arcade Learning Environment [, 2013] all feature a known initial (RAM) state and actions that have deterministic effects. Classical planners, however, cannot be used off-the-shelf as there is no compact PDDL-model of the games, and action effects and goals are not known a priori. Indeed, there are no explicit goals, and the planner must select actions on-line while interacting with a simulator that returns successor states and rewards. None of this precludes the use of blind lookahead algorithms for action selection like breadth-first search or Dijkstra's yet such methods are not effective over large state spaces. We thus turn to a different class of planning methods introduced recently that have been shown to be effective for solving large planning problems but which do not require prior knowledge of state transitions, costs (rewards) or goals. The empirical results over 54 Atari games show that the simplest such algorithm performs at the level of UCT, the state-of-the-art planning method in this domain, and suggest the potential of width-based methods for planning with simulators when factored, compact action models are not available. We consider multi-player repeated games involving a large number of players with large strategy spaces and enmeshed utility structures. In these ldquolarge-scalerdquo games, players are inherently faced with limitations in both their observational and computational capabilities. Accordingly, players in large-scale games need to make their decisions using algorithms that accommodate limitations in information gathering and processing. This disqualifies some of the well known decision making models such as ldquoFictitious Playrdquo (FP), in which each player must monitor the individual actions of every other player and must optimize over a high dimensional probability space. We will show that Joint Strategy Fictitious Play (JSFP), a close variant of FP, alleviates both the informational and computational burden of FP. Furthermore, we introduce JSFP with inertia, i.e., a probabilistic reluctance to change strategies, and establish the convergence to a pure Nash equilibrium in all generalized ordinal potential games in both cases of averaged or exponentially discounted historical data. We illustrate JSFP with inertia on the specific class of congestion games, a subset of generalized ordinal potential games. In particular, we illustrate the main results on a distributed traffic routing problem and derive tolling procedures that can lead to optimized total traffic congestion.