ECCC-Report TR22-018https://eccc.weizmann.ac.il/report/2022/018Comments and Revisions published for TR22-018en-usWed, 16 Feb 2022 00:05:13 +0200
Paper TR22-018
| Further Collapses in TFNP |
Mika Göös,
Alexandros Hollender,
Siddhartha Jain,
Gilbert Maystre,
William Pires,
Robert Robere,
Ran Tao
https://eccc.weizmann.ac.il/report/2022/018We 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.Wed, 16 Feb 2022 00:05:13 +0200https://eccc.weizmann.ac.il/report/2022/018