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MathGroup Archive 2005

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Re: boolean function, interpolation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg61567] Re: boolean function, interpolation
  • From: Maxim <ab_def at prontomail.com>
  • Date: Sat, 22 Oct 2005 03:24:06 -0400 (EDT)
  • References: <dj2719$bgb$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

On Tue, 18 Oct 2005 07:08:25 +0000 (UTC), edi <esolakster at gmail.com> wrote:

> Hi,
>
> I would like to interpolate vectors (dimension:20-30 bits) over GF(2)
> and values (one bit)to a function (boolean). Is there easy way to this
> in Mathematica?
>
> Thanks.
>

If you just want to create a function which takes given values on given  
boolean vectors, it is not hard:

In[1]:=
boolint[Lvecval_] := Module[
   {conj},
   conj[Lbool_] := Times @@ MapThread[
     If[# == 0, 1 - #2, #2]&,
     {Lbool, Array[Slot, Length@ Lbool]}];
   Total@ Cases[Lvecval, {v_, 1} :> conj[v]] //
     Evaluate // Function
]

In[2]:=
boolint[{{{0, 0, 0}, 1}, {{0, 1, 0}, 0}, {{1, 1, 1}, 1}}]

Out[2]=
(1 - #1)*(1 - #2)*(1 - #3) + #1*#2*#3&

We have constructed a function f such that

f[0, 0, 0] == 1
f[0, 1, 0] == 0
f[1, 1, 1] == 1

Maxim Rytin
m.r at inbox.ru


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