Further Collapses in \(\boldsymbol{\mathsf{TFNP}}\)

.We show \(\mathsf{EOPL}=\mathsf{PLS}\cap \mathsf{PPAD}\). Here the class \(\mathsf{EOPL}\) 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 \(\mathsf{CLS}=\mathsf{PLS}\cap \mathsf{PPAD}\) by Fearnley et al. (STOC 2021). We also prove a companion result \(\mathsf{SOPL}=\mathsf{PLS}\cap \mathsf{PPADS}\), where \(\mathsf{SOPL}\) is the class associated with the Sink-of-Potential-Line problem.KeywordsTFNPPLSPPADEOPLMSC codes68Q15