A computer is provided with a geometric representation of an as-designed part and a set of hybrid manufacturing capabilities. The computer computes a set of additive and subtractive manufacturing primitives from the provided set of hybrid manufacturing capabilities, and intersects the primitives to generate an atomic decomposition of space. The computer uses the atomic decomposition to generate a non-geometric representation of a space of manufacturable parts with hybrid manufacturing capabilities in at least one of symbolic, logical, and combinatorial forms. At least one of a necessary, sufficient, or necessary-and-sufficient condition for manufacturability is tested via examining the non-geometric representation for the existence of at least one feasible process plan whose outcome is an as-manufactured part that is interchangeable with the as-designed part.