For every Boolean f, bounded-error quantum and classical deterministic communication complexity of f ∘ AND₂ are polynomially related up to polylog n, both characterized by log of De Morgan sparsity of f.
An Average-Case Depth Hierarchy Theorem for Boolean Circuits , year =
3 Pith papers cite this work. Polarity classification is still indexing.
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An oracle exists relative to which TAUT has neither optimal proof systems nor recursive jump operators (even with infinite PH), showing Khaniki's question is not relativizably provable.
Explicit functions on {0,1}^n require ReLU networks of depth d to have width satisfying w^d = Omega(2^n) for exact computation.
citing papers explorer
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Quantum-Classical Equivalence for AND-Functions
For every Boolean f, bounded-error quantum and classical deterministic communication complexity of f ∘ AND₂ are polynomially related up to polylog n, both characterized by log of De Morgan sparsity of f.
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Recursive Jump Operators and Optimal Proof Systems
An oracle exists relative to which TAUT has neither optimal proof systems nor recursive jump operators (even with infinite PH), showing Khaniki's question is not relativizably provable.
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Depth Lower Bounds for ReLU Networks with Binary Inputs
Explicit functions on {0,1}^n require ReLU networks of depth d to have width satisfying w^d = Omega(2^n) for exact computation.