Linearization of multi-output logic functions by ordering of the autocorrelation values

Abstract

The paper deals with the problem of linear decomposition of a system of Boolean functions. A novel analytic method for linearization, by reordering the values of the autocorrelation function, is presented. The computational complexity of the linearization procedure is reduced by performing calculations directly on a subset of autocorrelation values rather than by manipulating the Boolean function in its initial domain. It is proved that unlike other greedy methods, the new technique does not increase the implementation cost. That is, it provides linearized functions with a complexity that is not greater than the complexity of the initial Boolean functions. Experimental results over standard benchmarks and random Boolean functions demonstrate the efficiency of the proposed procedure in terms of the complexity measure and the execution time.

Index Generation Functions: Recent Developments

“…And, autocorrelation was used to estimate the cost of the function. Recently, linear transformation is considered in [6] to reduce circuit complexity. In these works, the methods seem to be effective for totally or partially symmetric functions, including adders.…”

Efficient calculation of the autocorrelation of Boolean functions with a large number of variables

“…The autocorrelation function has numerous applications in computing, telecommunications, data encoding and transmission, cryptography, etc. In particular, in computer-aided design, the autocorrelation is used in the optimization and synthesis of combinational logic [1][2][3][4][5], variable ordering for binary decision diagrams [6][7][8][9], and estimation the function complexity [10]. The related algorithms are deterministic and, for the classes of Boolean functions where they can be efficiently applied (depending on the properties of autocorrelation coefficients), the produced solutions are optimal.…”