Further Collapses in TFNP
Mika G\"o\"os, Alexandros Hollender, Siddhartha Jain, Gilbert Maystre,, William Pires, Robert Robere, Ran Tao

TL;DR
This paper proves that the complexity class EOPL equals the intersection of PLS and PPAD, simplifying the understanding of total search problems and providing new insights into the collapse of related classes.
Contribution
It establishes the equality EOPL=PLS∩PPAD and offers a simpler proof of the collapse CLS=PLS∩PPAD, advancing the theoretical understanding of total search problem classes.
Findings
EOPL equals PLS intersect PPAD
Simplified proof of CLS collapse
Introduces the class SOPL and its relation to PLS and PPADS
Abstract
We show . Here the class 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 by Fearnley et al. (STOC 2021). We also prove a companion result , where is the class associated with the Sink-of-Potential-Line problem.
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