1. Binary Decision Diagrams Introduced by Lee (1959). Popularized by Bryant (1986). Graph-based Representation of Boolean Functions compact (functions of 50 variables) efficient (linear time manipluation) Widely used; has had a significant impact on the CAD industry. 0 1 1 0

2. Binary Decision Diagrams 0 1 1 0 1111 0 0 0 0 1 1 1 0 0 1 1 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 1 1 1 x 2 x 3 x f 0 1 BDD is defined as Directed Acyclic Graph Graph-based Representation of Boolean Functions

3. Binary Decision Diagrams Short described a cyclic structure for a BDD variant (1960). We suggest cycles are a general phenomenon. 001011

4. Binary Decision Diagrams Short described a cyclic structure for a BDD variant (1960). We suggest cycles are a general phenomenon. 001011 0 ** 0 0 1011 1

5. Binary Decision Diagrams Short described a cyclic structure for a BDD variant (1960). We suggest cycles are a general phenomenon. 001011

6. Binary Decision Diagrams Short described a cyclic structure for a BDD variant (1960). We suggest cycles are a general phenomenon. 001011 Future research awaits...