The classification of Boolean functions using the Rademacher-Walsh transform




Anderson, Neil Arnold

Journal Title

Journal ISSN

Volume Title



When considering Boolean switching functions with n input variables, there are 2^(2^n) possible functions that can be realized by enumerating all possible combinations of input values and arrangements of output values. As is expected with double exponential growth, the number of functions becomes unmanageable very quickly as n increases. This thesis develops a new approach for computing the spectral classes where the spectral operations are performed by manipulating the truth tables rather than first moving to the spectral domain to manipulate the spectral coefficients. Additionally, a generic approach is developed for modeling these spectral operations within the functional domain. The results of this research match previous for n < or = to 4 but differ when n=5 is considered. This research indicates with a high level of confidence that there are in fact 15 previously unidentified classes, for a total of 206 spectral classes needed to represent all 2^(2^n) Boolean functions.



Spectral Classification, Rademacher-Walsh Transform, Digital Logic, Boolean Functions, NPN Classes