PSPACE-Complete Two-Color Placement Games
Kyle Burke, Bob Hearn
TL;DR
This paper proves that three two-player placement games—Col, NoGo, and Fjords—are computationally complex (PSPACE-complete) even on planar graphs, highlighting their inherent difficulty in determining winning strategies.
Contribution
The paper establishes PSPACE-completeness for Col, NoGo, and Fjords on planar graphs, with reductions from Bounded 2-Player Constraint Logic and direct hardness proofs.
Findings
Col and Fjords are PSPACE-complete via reduction from Bounded 2-Player Constraint Logic.
NoGo is PSPACE-complete, directly reduced from Col.
Complexity results hold even on planar graphs.
Abstract
We show that three placement games, Col, NoGo, and Fjords, are PSPACE-complete on planar graphs. The hardness of Col and Fjords is shown via a reduction from Bounded 2-Player Constraint Logic and NoGo is shown to be hard directly from Col.
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Taxonomy
TopicsArtificial Intelligence in Games · Constraint Satisfaction and Optimization · Logic, programming, and type systems