On the Complexity and Optimization of Branching Programs for Decision Diagram Machines

Decision Diagram Machines (DDMs) are special purpose processors that evaluate decision diagrams. First, this paper derives upper bounds on the cost of multi-terminal binary decision diagrams (MTBDDs) for multiple-output logic functions. From these bounds we can estimate the size of branching programs running on various DDMs. Second, optimization of heterogeneous branching programs is undertaken that makes the area-time trade-off between the amount of memory required for a branching program and its execution time. As a case study, optimal architectures of branching programs are found for a set of benchmark tasks. Beside DDMs, the technique can also be used for micro-controllers with a support for multi-way branching running logic-intensive embedded firmware.