Hierarchical Information Patterns and Distributed Strategy Synthesis [chapter]

Dietmar Berwanger, Anup Basil Mathew, Marie van den Bogaard
2015 Lecture Notes in Computer Science  
Infinite games with imperfect information tend to be undecidable unless the information flow is severely restricted. One fundamental decidable case occurs when there is a total ordering among players, such that each player has access to all the information that the following ones receive. In this paper we consider variations of this hierarchy principle for synchronous games with perfect recall, and identify new decidable classes for which the distributed synthesis problem is solvable with
more » ... -state strategies. In particular, we show that decidability is maintained when the information hierarchy may change along the play, or when transient phases without hierarchical information are allowed. surveys on results in this direction, see e.g., the article [5] of Gastin, Sznajder, and Zeitoun, and the thesis of Puchala [15] . One fundamental case in which the distributed synthesis problem becomes decidable is that of hierarchical systems: these correspond to games where there is a total order among the players such that, informally speaking, each player has access to the information received by the players that come later in the order. Peterson and Reif [13] showed that for games in this setting, it is decidable whether distributed winning strategies exist -although, with nonelementary complexity -, and if yes, finite-state winning strategies can be effectively synthesised. The result was extended by Pnueli and Rosner [14] to the framework of distributed systems over fixed linear architectures where information can flow only in one direction. Later, Kupferman and Vardi developed a fundamental automata-theoretic approach [11] that allows to extend the decidability result from linear-time to branching-time specifications, and also removes some of the syntactic restrictions imposed by the fixed-architecture setting of Pnueli and Rosner. Finally, Finkbeiner and Schewe [4] give an effective characterisation of communication architectures on which distributed synthesis is decidable. The criterion requires absence of information forks, which implies a hierarchical order in which processes, or players, have access to the observations provided by the environment.
doi:10.1007/978-3-319-24953-7_28 fatcat:axov2fthorhidaovqhr65ao7xe