On Decision Diagrams for Maximally Asymmetric Functions
Shinobu Nagayama, Tsutomu Sasao, Jon T. Butler · 2022
Maximally asymmetric functions are multiple-valued functions such that “asymmetry” defined by the minimum Hamming distance from symmetric functions is maximum. While many studies on symmetric functions have been reported, few studies on maximally asymmetric functions have been reported. It is said that maximally asymmetric functions can be promising for applications such as CDMA communication and encryption, due to randomness of the functions. To promote related studies, providing benchmark maximally asymmetric functions in compact form is important. This paper focuses on decision diagrams as compact form of maximally asymmetric functions, and shows sizes of popular decision diagrams for the functions. This paper also presents a method to randomly generate benchmark maximally asymmetric functions represented by the decision diagrams.