ROBDD complexity analysis for XOR/XNOR min-terms

Abstract

This paper discusses the complexity of reduced ordered binary decision diagrams (ROBDDs) for Boolean functions with XOR/XNOR min-terms. Knowing the number of variables and the number of product terms of Boolean function containing only XOR/XNOR min-terms, one can predict the number of nodes in its ROBDD representation without building the binary decision diagram (BDD). A mathematical model for this prediction has been developed. This model can be used to find the maximum number of nodes for a given number of variables. Theoretical and experimental results are reported to underline the efficiency of this approach. The experimental results show that even though the XOR/XNOR min-terms cannot be simplified using Boolean laws or any other simplification method leading to a better min-term representation, the ROBDD will perform the simplification using the ROBDD reduction rules. The required memory is analysed for different methods of representation, and this analysis showed that ROBDDs are memory efficient structures to store and represent large numbers of XOR/XNOR min-terms in Boolean functions.