Further Collapses in TFNP

Authors Mika Göös, Alexandros Hollender , Siddhartha Jain , Gilbert Maystre, William Pires, Robert Robere , Ran Tao

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Author Details

Mika Göös
  • EPFL, Lausanne, Switzerland
Alexandros Hollender
  • University of Oxford, UK
Siddhartha Jain
  • EPFL, Lausanne, Switzerland
Gilbert Maystre
  • EPFL, Lausanne, Switzerland
William Pires
  • McGill University, Montreal, Canada
Robert Robere
  • McGill University, Montreal, Canada
Ran Tao
  • McGill University, Montreal, Canada


We thank Aviad Rubinstein for his many questions during e-mail correspondence, and the anonymous reviewers for their suggestions that helped improve the presentation of the paper.

Cite AsGet BibTex

Mika Göös, Alexandros Hollender, Siddhartha Jain, Gilbert Maystre, William Pires, Robert Robere, and Ran Tao. Further Collapses in TFNP. In 37th Computational Complexity Conference (CCC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 234, pp. 33:1-33:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


We 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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Complexity classes
  • Theory of computation → Problems, reductions and completeness
  • TFNP
  • PPAD
  • PLS
  • EOPL


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