Boolean Functions
Jon Awbrey
jawbrey at oakland.edu
Tue Apr 1 17:07:44 CEST 2003
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sorry, didn't look up the seq you mentioned, only saw the one that neil posted --
and now that i look at it again, not sure if it's Z_(2^n) or (Z_2)^n, where Z = C,
that was intended. my point was merely that in many applications, where binaries
are being used as codes for arbitrary objects, it's not always natural to assume
that those objects form a vector space. so we have to consider arbitrary code
transformations f : B* -> B*, where * is the kleene star. the linear analysis
of those transformations, logical analogues of taylor series into local linear
components, can be interesting, but it is usually only one form of analysis
that may be considered.
incidental musement:
http://www.altheim.com/cs/difflogic.html
at note 7 there is an exposition of the klein 4-group acting on {B^2 -> B},
serving to illustrate the wonderful world of "boolean difference calculus".
april fishes!
jon awbrey
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Gordon Royle wrote:
>
> > here you are taking a linear view of the spaces B^k and B^k -> B,
> > which may be natural in some applications but unnatural in others.
>
> Yes, I can see that in some applications, the linear point of view may not be
> the most natural. However, when one is using the general LINEAR group GL(n,2)
> to determine equivalence, surely the linear point of view is the most natural one...
>
> --
> Dr. Gordon F Royle, http://www.csse.uwa.edu.au/~gordon, gordon at csse.uwa.edu.au
> --
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