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We introduce a new BDD-like data structure called hybrid-restriction diagrams (HRDs) for the representation and manipulation of linear hybrid automata (LHA) state-spaces and present algorithms for weakest precondition calculations. This permits us to reason about the valuations of parameters that make safety properties satisfied. Advantages of our approach include the ability to represent discrete state information and concave polyhedra in a unified scheme, as well as to save both memory consumptions and manipulation times when processing the same substructures in state-space representations. Our experimental results document its efficiency in practice.