In the first case the lookahead is of finite possibly unbounded size, whereas in the second case it is of bounded size. We distinguish strategies with different degrees of lookahead, among them being the continuous and the bounded lookahead strategies. when buffers are present in communication or when signal transmission between components is deferred. This captures situations in distributed systems, e.g. The second player may postpone a move for a finite number of steps, or, in other words, exploit in his strategy some lookahead on the moves of the opponent. We study variants of regular infinite games where the strict alternation of moves between the two players is subject to modifications. Additionally, we prove that the same holds if the property is given by a monadic second-order formula to be evaluated on the limit of the evolution of the system. We show that for the considered class of rules and this logic, it can be decided whether the controller has a strategy ensuring a given property, and in such case a finite-memory strategy can be synthesised. To counter this restrictiveness, we allow the property to be ensured by the controller to be specified in a very expressive logic: a combination of monadic second-order logic evaluated on states and the modal mu-calculus for the temporal evolution of the whole system. We focus on one particular class of structure rewriting rules, namely on separated structure rewriting, a limited syntactic class of rules. Both the environment and the controller are allowed to change the structure in this way, and the question we ask is how a strategy for the controller that ensures a given property can be synthesised. We study systems in which a state is described by an arbitrary finite structure, and changes of the state are represented by structure rewriting rules, a generalisation of term and graph rewriting. The description of a single state of a modelled system is often complex in practice, but few procedures for synthesis address this problem in depth.
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