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   sci.math.symbolic      Symbolic algebra discussion      10,432 messages   

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   Message 8,492 of 10,432   
   acd to All   
   Equivalence relation on Boolean vectors   
   06 Jan 14 23:40:36   
   
   From: acd4usenet@lycos.de   
      
   I have recently completed some work on   
   configurable circuits for rotationally symmetric Boolean functions.   
      
   That means functions, such that   
   if x is equivalent with y   
   f(x) = f(y).   
      
   x and y are equivalent if x can be cyclically shifted into y:   
   x=(x_1,x_2,...x_n)   
   y = (x_k,...x_n,x_1,..x_k-1)   
      
   This has the consequence that the input space {0,...,2^n-1}   
   is divided into classes of roughly n elements (the necklace problem   
   has the details).   
      
   To test my circuit generation approach further I would like   
   to use a different equivalence relation, that is neither based on   
   "arithmetic" nor on bit permutations, and which has larger equivalence classes,   
   something like 2^(n/2).   
      
   With "arithmetic" I mean something like   
   x mod h   
   where h = 2^(n/2).   
      
   Any ideas?   
      
   Andreas   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)   

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