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Re: Boolean factorization

  • To: mathgroup at smc.vnet.net
  • Subject: [mg113113] Re: Boolean factorization
  • From: Daniel Lichtblau <danl at wolfram.com>
  • Date: Wed, 13 Oct 2010 12:39:56 -0400 (EDT)
  • References: <201010121748.NAA03419@smc.vnet.net>

olfa wrote:
> Hi Mathematica Community,
> 
> How to factorize
> (a && b && c && d && e && f) || (a && b && c && d && g && h) || (a &&
> b && c && d && i && j)
> into
> a && b && c && d && ((e&&f) || (g&&h) || (i && j))
> 
> Thank you.

One approach is to form the CNF, then split out parts with Or, form a 
DNF thereof, and rejoin.

ii = (a && b && c && d && e && f) || (a && b && c && d && g && h) ||
    (a && b && c && d && i && j);
jj = BooleanMinimize[ii, "CNF"];
jjOr = Cases[jj, Or[_,__]];
jjnoOr = DeleteCases[jj, Or[_,__]];

In[14]:= new = And[jjnoOr, BooleanMinimize[And@@jjOr]]
Out[14]= a && b && c && d && ((e && f) || (g && h) || (i && j))

Daniel Lichtblau
Wolfram Research



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