Vexing Vexillological Logic
Kyle Burke, Craig Tennenhouse

TL;DR
This paper introduces a new combinatorial game called Flag Coloring, analyzes its complexity, and explores its outcomes on real-world flags, revealing its PSPACE-completeness for multiple colors.
Contribution
It defines a novel flood-filling based game, generalizes it to graphs, and proves its PSPACE-completeness for two or more colors, also analyzing real-world flag scenarios.
Findings
The game is PSPACE-complete for two or more colors.
Outcome classes are determined for flag-based positions.
Many positions on two colors have known values.
Abstract
We define a new impartial combinatorial game, Flag Coloring, based on flood filling. We then generalize to a graph game, and find values for many positions on two colors. We demonstrate that the generalized game is PSPACE-complete for two colors or more via a reduction from Avoid True, determine the outcome classes of games based on real-world flags, and discuss remaining open problems.
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Taxonomy
TopicsArtificial Intelligence in Games · Logic, Reasoning, and Knowledge · Advanced Database Systems and Queries
