English

Strings-and-Coins and Nimstring are PSPACE-complete

Computational Complexity 2023-10-27 v2 Combinatorics

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.

Cite

@article{arxiv.2101.06361,
  title  = {Strings-and-Coins and Nimstring are PSPACE-complete},
  author = {Erik D. Demaine and Jenny Diomidova},
  journal= {arXiv preprint arXiv:2101.06361},
  year   = {2023}
}

Comments

10 pages, 7 figures. Improved wording and figures; cite arXiv:2105.02837

R2 v1 2026-06-23T22:13:19.282Z