We show EOPL=PLS∩PPAD. Here the class 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 CLS=PLS∩PPAD by Fearnley et al. (STOC 2021). We also prove a companion result SOPL=PLS∩PPADS, where SOPL is the class associated with the Sink-of-Potential-Line problem.
Cite
@article{arxiv.2202.07761,
title = {Further Collapses in TFNP},
author = {Mika Göös and Alexandros Hollender and Siddhartha Jain and Gilbert Maystre and William Pires and Robert Robere and Ran Tao},
journal= {arXiv preprint arXiv:2202.07761},
year = {2022}
}