Did the Train Reach its Destination: The Complexity of Finding a Witness

TL;DR

This paper investigates the computational complexity of finding witnesses for termination in a switch graph game, showing that the search problem is in PLS, which advances understanding of the problem's difficulty.

Contribution

It demonstrates that the search version of the game, finding witnesses for termination or non-termination, is in the complexity class PLS, providing new insights into its computational complexity.

Findings

The decision problem is in NP ∩ coNP.

The search problem is in PLS.

Provides complexity classification for the witness-finding task.

Abstract

Recently, Dohrau et al. studied a zero-player game on switch graphs and proved that deciding the termination of the game is in NP $\cap$ coNP. In this short paper, we show that the search version of this game on switch graphs, i.e., the task of finding a witness of termination (or of non-termination) is in PLS.