If Cui 2n then fX has a decomposition

1
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