Strings-and-Coins and Nimstring are PSPACE-complete
Erik D. Demaine, Jenny Diomidova

TL;DR
This paper proves that the combinatorial game Strings-and-Coins, which generalizes Dots-and-Boxes, is strongly PSPACE-complete on multigraphs, improving previous NP-hardness results and also applying to Nimstring variants.
Contribution
It establishes the PSPACE-completeness of Strings-and-Coins and Nimstring, providing a stronger complexity classification than prior NP-hardness results.
Findings
Strings-and-Coins is strongly PSPACE-complete.
The PSPACE-completeness applies to multigraphs.
The result extends to Nimstring variants.
Abstract
We prove that Strings-and-Coins -- the combinatorial two-player game generalizing the dual of Dots-and-Boxes -- is strongly PSPACE-complete on multigraphs. This result improves the best previous result, NP-hardness, argued in Winning Ways. Our result also applies to the Nimstring variant, where the winner is determined by normal play; indeed, one step in our reduction is the standard reduction (also from Winning Ways) from Nimstring to Strings-and-Coins.
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Taxonomy
TopicsArtificial Intelligence in Games · Sports Analytics and Performance · Gambling Behavior and Treatments
