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Randomized Algorithm On input polynomials pi and p2: d=max{deg(p),deg(p2)} a1,,an←R{1,2,…,100d Evaluate p1(ai,…,an)andp2(a1,…,an)by running the circuits on (a,...an). ■ifp1(a1,…,an)=p2(a1,,an), output“p1=p2". else output“p1≠p2”. 10Randomized Algorithm On input polynomials 𝑝1 and 𝑝2: ◼ 𝑑 = max{deg(𝑝1),deg(𝑝2)} ◼ 𝑎1, …, 𝑎𝑛 ←𝑅 {1,2, … , 100𝑑} ◼ Evaluate 𝑝1(𝑎1,…, 𝑎𝑛) and 𝑝2(𝑎1,…, 𝑎𝑛) by running the circuits on (𝑎1,… , 𝑎𝑛). ◼ if 𝑝1 𝑎1,…, 𝑎𝑛 = 𝑝2(𝑎1,… , 𝑎𝑛), output “ 𝑝1 = 𝑝2”. else output “ 𝑝1 ≠ 𝑝2”. 10
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