Consensus Game Acceptors And Iterated Transductions

We study a game for recognising formal languages, in which two players with imperfect information should coordinate on a common decision, given private input words correlated by a finite graph. The players have a common objective to avoid an inadmissible decision, in spite of the uncertainty induced by the input.We show that the acceptor model based on consensus games characterises context sensitive languages. Further, we describe the expressiveness of these games in terms of iterated synchronous transductions and identify a subclass that characterises context-free languages.