变迁系统 transition system

transition system本质上就是带有标记的有向图。

Formally, a transition system is a pair (S, →) where S is a set of states and → is a relation of state transitions (i.e., a subset of S × S). A transition from state p to state q, i.e. (p, q) ∈ →, is written as p → q.

标记可以在节点、边上,或两者皆有。

A labelled transition system is a tuple (S, Λ, →) where S is a set of states, Λ is a set of labels and → is a relation of labelled transitions (i.e., a subset of S × Λ × S).

标记在节点上的transition system也就是 Kripke Structure。FA和 ω-automata 也可以认为是标记在边上的transition system,但是表达能力更高的自动机并不单纯是一张标记图。

有时,transition system也有初始状态集I。而所谓终止状态集F,即那些没有转移的状态(对任意label)的集合。