1. A method for generating a pattern database for a model-based control system, wherein said model-based control system includes a directed acyclic graph, wherein the directed acyclic graph includes a plurality of vertices interconnected by a plurality of edges, wherein each of the plurality of vertices includes a range set, said method comprising the steps of: (a) propagating the range sets of each of the plurality of vertices in a bottom-up order, wherein each of the propagated range sets is propagated from a source vertex to an immediate ancestor over an edge, wherein the range set of at least one of the plurality of vertices includes a plurality of intervals; (b) adding the each of the propagated range sets to the range set of the immediate ancestor corresponding to the each of the propagated range sets.