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Paper:

TR23-073 | 15th May 2023 21:15

Reducing Tarski to Unique Tarski (in the Black-box Model)

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TR23-073
Authors: Xi Chen, Yuhao Li, Mihalis Yannakakis
Publication: 21st May 2023 05:59
Downloads: 312
Keywords: 


Abstract:

We study the problem of finding a Tarski fixed point over the $k$-dimensional grid $[n]^k$. We give a black-box reduction from the Tarski problem to the same problem with an additional promise that the input function has a unique fixed point. It implies that the Tarski problem and the unique Tarski problem have exactly the same query complexity. Our reduction is based on a novel notion of partial-information functions which we use to fool algorithms for the unique Tarski problem as if they were working on a monotone function with a unique fixed point.



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