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The work on GDSs considers finite graphs and finite state spaces. As such, the research typically involves techniques from, e.g., graph theory, combinatorics, algebra, and dynamical systems rather than differential geometry. In principle, one could define and study GDSs over an infinite graph (e.g. cellular automata or probabilistic cellular automata over <math>\mathbb{Z}^k</math> or interacting particle systems when some randomness is included), as well as GDSs with infinite state space (e.g. <math>\mathbb{R}</math> as in coupled map lattices); see, for example, Wu. In the following, everything is implicitly assumed to be finite unless stated otherwise.

The work on GDSs considers finite graphs and finite state spaces. As such, the research typically involves techniques from, e.g., graph theory, combinatorics, algebra, and dynamical systems rather than differential geometry. In principle, one could define and study GDSs over an infinite graph (e.g. cellular automata or probabilistic cellular automata over <math>\mathbb{Z}^k</math> or interacting particle systems when some randomness is included), as well as GDSs with infinite state space (e.g. <math>\mathbb{R}</math> as in coupled map lattices); see, for example, Wu. In the following, everything is implicitly assumed to be finite unless stated otherwise.

Gdss 的工作是研究有限图和有限状态空间。因此，研究通常涉及到的技术，如[[图论]]，[[组合学]]，[[代数]]和[[动力系统]]，而不是微分几何。原则上，我们可以在一个无限图上定义和研究 gds (例如:。元胞自动机或概率元胞自动机在 math  mathbb { z } ^ k / math 或相互作用的粒子系统(包括一些随机性)上，以及具有无限状态空间的 gds (例如:。在耦合映象格子中的 math  mathbb { r } / math) ; 例如，见 Wu。在下文中，除非另有说明，否则一切都默认为有限。

Gdss 的工作是研究有限图和有限状态空间。因此，研究通常涉及到的技术是[[图论]]，[[组合学]]，[[代数]]和[[动力系统]]，而不是微分几何。原则上，我们可以在一个无限图上定义和研究 gds (例如:。元胞自动机或概率元胞自动机在 math  mathbb { z } ^ k / math 或相互作用的粒子系统(包括一些随机性)上，以及具有无限状态空间的 gds (例如:在耦合映象格子中的 math  mathbb { r } / math) ; 例如，见 Wu。在下文中，除非另有说明，否则一切图和空间都默认为有限。

==Formal definition正式定义==

==Formal definition 正式定义==