On the Optimal OBDD Representation of 2-XOR Boolean Affine Spaces

A Reduced Ordered Binary Decision Diagram (ROBDD) is a data structure widely used in an increasing number of fields of Computer Science. In general, ROBDD representations of Boolean functions have a tractable size, polynomial in the number of input variables, for many practical applications. However, the size of a ROBDD, and consequently the complexity of its manipulation, strongly depends on the variable ordering: depending on the initial ordering of the input variables, the size of a ROBDD representation can grow from linear to exponential. In this paper, we study the ROBDD representation of Boolean functions that describe a special class of Boolean affine spaces, which play an important role in some logic synthesis applications. We first discuss how the ROBDD representations of these functions are very sensitive to variable ordering, and then provide an efficient linear time algorithm for computing an optimal variable ordering that always guarantees a ROBDD of size linear in the number of input variables.