论文标题
同步线性约束系统游戏
Synchronous linear constraint system games
论文作者
论文摘要
同步线性约束系统游戏是非本地游戏，可验证两个玩家是否共享给定方程系统的解决方案。与这些游戏相关的两个代数对象编码有关存在完美策略的信息。它们被称为游戏代数和解决方案组。在这里，我们表明这些对象基本相同，即游戏代数是解决方案组的组代数的合适商。我们还证明了线性约束系统游戏等效于通过线性系统参数为参数的图形同构游戏。
Synchronous linear constraint system games are nonlocal games that verify whether or not two players share a solution to a given system of equations. Two algebraic objects associated to these games encode information about the existence of perfect strategies. They are called the game algebra and the solution group. Here we show that these objects are essentially the same, i.e., that the game algebra is a suitable quotient of the group algebra of the solution group. We also demonstrate that linear constraint system games are equivalent to graph isomorphism games on a pair of graphs parameterized by the linear system.
