A Dual Polynomial for OR

We reprove that the approximate degree of the OR function on n bits is ( n). We consider a linear program which is feasible if and only if there is an approximate polynomial for a given function, and apply the duality theory. The duality theory says that the primal program has no solution if and only if its dual has a solution. Therefore one can prove the nonexistence of an approximate polynomial by exhibiting a dual solution, coined the dual polynomial. We construct such a polynomial.

• Type: Journal
• Year: 2008
• Where: CORR
• Authors: Robert Spalek
• Keywords: Approximate Degree, Approximate Polynomial, CORR 2008, Duality Theory, Education