Göös, MikaHollender, AlexandrosJain, SiddharthaMaystre, GilbertPires, WilliamRobere, RobertTao, Ran2023-01-172023-01-172023-01-17202210.4230/lipics.ccc.2022.33https://infoscience.epfl.ch/handle/20.500.14299/193989We 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 Hubáček 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. LIPIcs, Vol. 234, 37th Computational Complexity Conference (CCC 2022), pages 33:1-33:15text::conference output::conference proceedings::conference paper