Further Collapses in TFNP

Mika Göös; Alexandros Hollender; Siddhartha Jain; Gilbert Maystre; William Pires; Robert Robere; Ran Tao

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arXiv · 2202.07761

Further Collapses in TFNP

Mika Göös·Alexandros Hollender·Siddhartha Jain·Gilbert Maystre·William Pires·Robert Robere·Ran Tao

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Abstract

We show $\textsf{EOPL}=\textsf{PLS}\cap\textsf{PPAD}$. Here the class $\textsf{EOPL}$ consists of all total search problems that reduce to the End-of-Potential-Line problem, which was introduced in the works by Hubacek and Yogev (SICOMP 2020) and Fearnley et al. (JCSS 2020). In particular, our result yields a new simpler proof of the breakthrough collapse $\textsf{CLS}=\textsf{PLS}\cap\textsf{PPAD}$ by Fearnley et al. (STOC 2021). We also prove a companion result $\textsf{SOPL}=\textsf{PLS}\cap\textsf{PPADS}$, where $\textsf{SOPL}$ is the class associated with the Sink-of-Potential-Line problem.

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Mika Göös, Alexandros Hollender, Siddhartha Jain, Gilbert Maystre, William Pires, Robert Robere, Ran Tao. 2022-02-15. Further Collapses in TFNP. https://arxiv.org/abs/2202.07761

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