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If C(u i ) = -2 n then f(X) has a decomposition

x 3 x 2 x 1. f(X). 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1. 0 1 1 0 0 1 0 0. B(u). u 3 u 2 u 1. 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1. 3 0 0 2 2 0 0 2. Autocorrelation Coefficients in the Representation and Classification of Switching Functions.

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If C(u i ) = -2 n then f(X) has a decomposition

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  1. x3x2x1 f(X) 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 0 1 1 0 0 1 0 0 B(u) u3u2u1 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 3 0 0 2 2 0 0 2 Autocorrelation Coefficients in the Representation and Classification of Switching Functions J. E. Rice, University of Lethbridge uses in three-level decompositions THEOREM 1 what are autocorrelation coefficients? If C(ui) = -2n then f(X) has a decomposition f(X) = f*(X)  xi where f*(X) is independent of xi. THEOREM 2 If C(ui) = C(uj) = C(uij) = 0, i ≠ j then f(X) has a decomposition f(X) = f*(X)  g(X) where g(X) = xi * xj, *  {∧,∨} and f*(X) is independent of both xi and xj. f(X) = (x1∨ x2x3)  (x4x5) EXAMPLE first order coefficients second order coefficients 00001 0 00010 0 00100 16 01000 16 10000 -16 00011 0 10001 0 00110 0 10010 0 01001 0 10100 -16 01100 16 11000 -16 RESULTS computation techniques • BDD-based techniques found to be very successful other uses • Work with the autocorrelation coefficients is continuing in many areas, including: • a new classification method for switching functions • determining KDD decomposition tables • - identification of symmetries • - identification of degenerate and sparse functions

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