Representing Subassembly Trees by Deepest Common Ancestor Relations

XAP/1 was a constraint-based planner designed to generate plans for the manufacture of mechanical assemblies. In order to extend it to be able to generate plans utilizing subassemblies the constraint language must be extended. It has been proposed elsewhere that deepest common ancestor relations can form the basis for such a system[1]. This report serves to provide a formal basis for the use of deepest common ancestor relations to represent subassembly tree plans. It rst de nes subassembly tree plans, and three kinds of assertions which use the notion of deepest common ancestors to describe a plan. The rules that must hold among a consistent set of assertions are derived. Finally, it is shown that a complete and consistent set of assertions must uniquely de ne a single subassembly tree plan.