This paper introduces a new data structure for representing Boolean functions using directed, acyclic graphs, similar to binary decision diagrams but with additional restrictions on the ordering of decision variables. The authors present a set of manipulation algorithms that are efficient in terms of time complexity, proportional to the size of the graphs being operated on. The algorithms are demonstrated through experimental results in logic design verification, showing their practicality. The paper also discusses the efficiency of the representation, noting that while some functions may require exponential graph sizes, most commonly encountered functions have more reasonable representations. The authors highlight the importance of choosing an appropriate input ordering to minimize graph size, as the ordering can significantly affect performance. The paper concludes with a discussion of the limitations of the approach, particularly for functions like integer multiplication, which can have exponentially large graphs regardless of input ordering.This paper introduces a new data structure for representing Boolean functions using directed, acyclic graphs, similar to binary decision diagrams but with additional restrictions on the ordering of decision variables. The authors present a set of manipulation algorithms that are efficient in terms of time complexity, proportional to the size of the graphs being operated on. The algorithms are demonstrated through experimental results in logic design verification, showing their practicality. The paper also discusses the efficiency of the representation, noting that while some functions may require exponential graph sizes, most commonly encountered functions have more reasonable representations. The authors highlight the importance of choosing an appropriate input ordering to minimize graph size, as the ordering can significantly affect performance. The paper concludes with a discussion of the limitations of the approach, particularly for functions like integer multiplication, which can have exponentially large graphs regardless of input ordering.