Exact OBDD Bounds for Some Fundamental Functions

Ordered binary decision diagrams (OBDDs) are nowadays one of the most common dynamic data structures or representation types for Boolean functions. Among the many areas of application are verification, model checking, computer aided design, relational algebra, and symbolic graph algorithms. Although many exponential lower bounds on the OBDD size of Boolean functions are known, there are only few functions where the OBDD size is asymptotically known exactly. In this paper the exact OBDD sizes of the fundamental functions multiplexer and addition of n-bit numbers are determined.