We give an algorithmic calculus of the reachability relations on clock values defined by timed automata. Our approach is a modular one, by computing unions, compositions and reflexive-transitive closure (star) of “atomic” relations. The essential tool is a new representation technique for n-clock relations – the 2n-automata – and our strategy is to show the closure under union, composition and star of the class of 2n-automata that represent reachability relations in timed automata.
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