Year: 2026
Type: preprint
Abstract: Poset games form a fundamental class of combinatorial games that includes classical games such as Nim and Chomp. Determining the outcome of a poset game is known to be PSPACE-complete even for posets of height at most three. However, the exact computational complexity of Two-Level Poset Game, played on posets of height at most two, has remained an open problem for over a decade. We resolve this problem by proving that Two-Level Poset Game is PSPACE-complete via a polynomial-time reduction from Avoid True on positive CNF formulas.
Source: arXiv (Cornell University)
Author: Hashimoto, Kengo
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221927926