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Espresso | Prime Number | Mathematical Logic

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Espresso algo digital electronic
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  1 Generalized Cofactor Definition 1 Let f, g   be completely specified functions. The generalized cofactor of f   with respect to  g   is the incompletely specified function: Definition 2 Let = ( f, d, r  ) and  g   be given. Then ),,(),(  g  f   g  g  f   g  f  co   ),,(),(  g r  g d  g  f   g co    2 Relation with Shannon Cofactor ã Let  g=x  i .  Shannon cofactor is ã Generalized cofactor with respect to  g=x  i   is ã Note that In fact f  x i   is the unique cover of co(f, x  i  )   independent of the variable x  i . ),),1(,,( 1  ni x  x x x f   f   i    ),,(),( iiii  x f   x x f   x f  co   iii xi  x f   x x f   f   x f   i   3 Shannon Cofactor ),,(),(  a f  aa f  a f  co   off on  Don’t care   a cbbc f   a   cbacbacbaabc f      4 Shannon Cofactor (Cont.)     a  f a f f a So a f     a  f    fa a     f   ),,(),(  a f  aa f  a f  co  
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