if c(u i ) = -2 n then f(x) has a decomposition
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
If C(ui) = -2n then f(X) has a decompositionf(X) = f*(X) xi where f*(X) is independent of xi.
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.
THEOREM 1
THEOREM 2
EXAMPLE f(X) = (x1 ∨ x2x3) (x4x5)
first order coefficients
00001 0 00010 0 00100 16 01000 1610000 -16
00011 0 10001 000110 0 10010 0 01001 0 10100 -16 01100 16 11000 -16
second order coefficients
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
uses in three-level
decompositions
other uses
Autocorrelation Coefficients in the Representation and Classification of Switching Functions
RESULTSsuccesses avg. time
xor logic detected
AOXMIN 244/278 71.1 sec 54
our method 278/278 5.4 sec 59
- BDD-based techniques found to be very successful
computation techniques
x3x2x1 f(X)
0 0 00 0 10 1 00 1 11 0 01 0 11 1 01 1 1
01100100
u3u2u1 B(u)
0 0 00 0 10 1 00 1 11 0 01 0 11 1 01 1 1
30022002
what are autocorrelation coefficients?
J. E. Rice, University of Lethbridge
best BDD technique
best bruteforce technique
10 or fewer inputs
0.02 sec 0.78 sec
11 to 30 inputs
1.00 sec 67.6 sec
31 or greater inputs
4.58 sec 663 sec