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Global constraints are an important tool in the constraint toolkit. Unfortunately, whilst it is usually easy to specify when a global constraint holds, it is often difficult to build a good propagator. One promising direction is to specify global constraints via grammars or automata. For example, the Regular constraint [1] permits us to specify a wide range of global constraints by means of a DFA accepting a regular language, and to propagate this constraint specification efficiently and effectively. More precisely, the Regular constraint ensures that the values taken by a sequence of variables form a string accepted by the DFA. In this paper, we consider how to propagate such grammar constraints and a number of extensions.