Superpolynomial lower bounds for multilinear algebraic branching programs

Establish superpolynomial lower bounds on the size of multilinear algebraic branching programs (mABPs) computing explicit multilinear polynomials; equivalently, prove that there exists an explicit polynomial in the class mVP that requires mABP size n^{ω(1)}, thereby separating mVBP from mVP.

Background

Multilinear formulas are known to require superpolynomial size for certain explicit polynomials by Raz, but extending such lower bounds to multilinear algebraic branching programs (mABPs) has resisted progress for decades. The best known mABP lower bounds remain near-quadratic, and all known approaches use the min-partition rank method, which this paper shows cannot yield superpolynomial mABP lower bounds. Consequently, proving such lower bounds necessitates new techniques beyond min-partition rank.