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TR23-039 | 28th March 2023 19:57

Query Complexity of Search Problems


Authors: Arkadev Chattopadhyay, Yogesh Dahiya, Meena Mahajan
Publication: 28th March 2023 21:07
Downloads: 195


We relate various complexity measures like sensitivity, block sensitivity, certificate complexity for multi-output functions to the query complexities of such functions. Using these relations, we improve upon the known relationship between pseudo-deterministic query complexity and deterministic query complexity for total search problems: We show that pseudo-deterministic query complexity is at most the third power of its deterministic query complexity. (Previously a fourth-power relation was shown by Goldreich,Goldwasser,Ron (ITCS13).) We then obtain a significantly simpler and self-contained proof of a separation between pseudodeterminism and randomized query complexity recently proved by Goldwasser, Impagliazzo, Pitassi, Santhanam (CCC 2021). We also separate pseudodeterminism from randomness in AND decision trees, and determinism from pseudodeterminism in PARITY decision trees. For a hypercube colouring problem closely related to the pseudodeterministic complexity of a complete problem in $TFNP^{dt}$, we prove that either the monotone block-sensitivity or the anti-monotone block sensitivity is $\Omega(n^{1/3})$; previously an $\Omega(n^{1/2})$ bound was known but for general block-sensitivity.

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