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 Hubacek and Yogev (SICOMP 2020) and Fearnley et al. (JCSS 2020).

Reconfiguring a system (generally represented by a graph) means gradually transforming one configuration of the system to another configuration by modifying it in a slow and steady step-by-step manner.

It is well known that the classic Los-Tarski preservation theorem fails in the finite: there are first order definable classes of finite structures closed under extensions which are not definable in the existential fragment of first order logic.

This talk is based on Tadashi Tokieda's wonderful talk (https://www.youtube.com/watchv=tQQ3oiB32GI&t=1s) as a part of ICTS's distinguished lecture series.