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.
The talk will be based on the following paper: https://eccc.weizmann.ac.il/report/2022/018/