Bo-Yu Liu

Dimension Amplification for Tarski Fixed-Point Query Lower Bounds

We prove that finding a fixed point of a monotone map on the nine-dimensional grid $[N]^9$ requires $\Omega((\log N)^3)$ deterministic queries, even when the fixed point is unique and each query returns the entire function value. The proof gives a construction that raises the dimension from $d$ to $4d+1$, preserves uni...