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Affine equivalence classification of Boolean functions has significant applications in logic synthesis and cryptography. Previous studies for classification have been limited by the large set of Boolean functions and the complex operations on the affine group. Although there are many research on affine equivalence classification for parts of Boolean functions in recent years, there are very few results for the entire set of Boolean functions. The best existing result has been achieved by Harrison with 15768919 affine equivalence classes for 6-variable Boolean functions. This paper presents a concise formula for affine equivalence classification of the entire set of Boolean functions as well as a formula for affine classification of Boolean functions with distinct ON-set size respectively. The method outlined in this paper greatly simplifies the affine group's action by constructing an isomorphism mapping from the affine group to a permutation group. By this method, we can compute the affine equivalence classes for up to 10 variables. Experiment results indicate that our scheme for calculating the affine equivalence classes for more than 6 variables is a significant advancement over previous published methods. [ABSTRACT FROM PUBLISHER]

Automatic hardware/software partitioning relies on characterization, estimation and design space exploration of the system performance and cost metrics. In real world situations, such estimates are complicated and cannot be 100 percent accurate. Furthermore, hardware/software co-design is so complicated nowadays that simply considering the bipartitioning between hardware and software is not sufficient. It is important to consider some of the other key design parameters and resource sharing together with the hardware/software partitioning problem. Under variable requirements of smart systems, more flexibility on the resource usage should be incorporated in system modelling. This paper considers uncertainty modeling for system partitioning with an enhanced set of parameters for hardware/software resource sharing. We harness state-of-the-art uncertainty theory for linear uncertain distribution and normal uncertain distribution. Our derivations convert the uncertainty model back to a regular constraint optimization problem. Experimental results show the effectiveness of our approach. [ABSTRACT FROM AUTHOR]