Reducing polynomial powers on Boolean inputs
When a variable X_i will be evaluated only at 0 or 1, any positive power X_i^k can be replaced by X_i without changing those evaluations. Apply this to every monomial and collect terms. The result is multilinear: each variable has exponent at most one in each term. Total degree cannot increase. For p(X,Y)=2+3X^2+5XY^3, the Boolean-equivalent form is 2+3X+5XY. This is equality on Boolean inputs, not equality of polynomials on arbitrary rational inputs. Here X,Y are auxiliary Boolean inputs; this rule does not permit simplifying the arbitrary replacement values inside H as though they were bits.
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Related
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A data analyst uses the polynomial expression 8x^2y^4 - 3x^3y + 12 to model the efficiency of a processing plant. Based on the definition of a polynomial's degree, what is the degree of this expression?
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