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Electronic Colloquium on Computational Complexity

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REPORTS > KEYWORD > PARITY BRANCHING PROGRAMS:
Reports tagged with parity branching programs:
TR26-115 | 7th July 2026
Ben Lee Volk

A Lower Bound for Read-Once Parity Branching Programs

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

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