Further Collapses in TFNP

02/15/2022

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by   Mika Göös, et al.

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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.