English

Further Collapses in TFNP

Computational Complexity 2022-05-23 v2

Abstract

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

Cite

@article{arxiv.2202.07761,
  title  = {Further Collapses in TFNP},
  author = {Mika Göös and Alexandros Hollender and Siddhartha Jain and Gilbert Maystre and William Pires and Robert Robere and Ran Tao},
  journal= {arXiv preprint arXiv:2202.07761},
  year   = {2022}
}
R2 v1 2026-06-24T09:39:56.947Z