Further Collapses in TFNP

We show EOPL = PLS \cap PsansP \sansP AD. 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 Hub'acv \ek 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 \cap PsansP \sansP AD by Fearnley et al. (STOC 2021). We also prove a companion result SOPL = PLS \cap PsansP \sansP ADS, where SOPL is the class associated with the SINK -OF -POTENTIAL -LINE problem.