A Lower Bound for Read-Once Parity Branching Programs

We prove an $\tilde{\mathrm{\Omega }}(n^2)$ lower bound for read-once parity branching programs computing an explicit boolean function on $n$ variables. The previous best lower bound was $\tilde{\mathrm{\Omega }}(n^{1.5})$. Our lower bound is proved by reducing the problem to a lower bound in algebraic circuit complexity.