Michela Ceria edited bits4.tex  about 6 years ago

Commit id: 6ebc283b21e83a654c3bc2ea971ceef4c122c4d5

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\[  \NOT(x\, \OR \, y)=\NOT(x)\, \AND\, \NOT(y)  \]  From this follows our $o(x,y)$ function we deduce that  $$  o(x, y)=\NOT(\NOT(x)\, y)=\NOT(\NOT(x\, \OR \, y))=\NOT(\NOT(x)\,  \AND\, \NOT(y)). $$  Translating in polynomials with coefficients in $\Fb$ we have Since  the operator $\AND$ corresponds to multiplication, the above formula becomes  \[  o(x,y)=(x+1)\times(y+1)+1. o(x,y)=\big((x+1)(y+1)\big)+1.  \]  That Wich  is after simplifications \[  o(x,y)=xy+x+y.  \]