no code implementations • 12 Sep 2021 • Kyle Burke, Matthew Ferland, ShangHua Teng
We prove that Generalized Geography is complete for the natural class, $\cal{I}^P$ , of polynomially-short impartial rulesets under nimber-preserving reductions, a property we refer to as Sprague-Grundy-complete.
no code implementations • 3 Jun 2021 • Kyle Burke, Matthew Ferland, ShangHua Teng
Additionally, we show, for the first time, how to construct Undirected Geography instances with Grundy value $\ast n$ and size polynomial in n. We strengthen a result from 1981 showing that sums of tractable partisan games are PSPACE-complete in two fundamental ways.
no code implementations • 18 Jan 2021 • Kyle Burke, Matthew Ferland, ShangHua Teng
In addition to analyzing the mathematical structures and computational complexity of Transverse Wave, we provide a web-based version of the game, playable at https://turing. plymouth. edu/~kgb1013/DB/combGames/transverseWave. html.
Computational Complexity Combinatorics 91A46 G.2.1; G.2.2; F.1.3
no code implementations • 7 Nov 2020 • Kyle Burke, Matthew Ferland, Shang-Hua Teng
The beauty of quantum games-succinct in representation, rich in structures, explosive in complexity, dazzling for visualization, and sophisticated for strategic reasoning-has drawn us to play concrete games full of subtleties and to characterize abstract properties pertinent to complexity consequence.
