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### Paper:

TR22-018 | 15th February 2022 22:26

#### Further Collapses in TFNP

TR22-018
Authors: Mika Göös, Alexandros Hollender, Siddhartha Jain, Gilbert Maystre, William Pires, Robert Robere, Ran Tao
Publication: 16th February 2022 00:05
We show $\text{EOPL}=\text{PLS}\cap\text{PPAD}$. Here the class $\text{EOPL}$ 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 $\text{CLS}=\text{PLS}\cap\text{PPAD}$ by Fearnley et al. (STOC 2021). We also prove a companion result $\text{SOPL}=\text{PLS}\cap\text{PPADS}$, where $\text{SOPL}$ is the class associated with the Sink-of-Potential-Line problem.