有限状态自动机

最新推荐文章于 2022-09-20 16:48:04 发布

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#二叉树

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习题 3.1 模仿自动机的样子来重新定义二叉树.

A deterministic finite state automata (DFA) is a 5-tuple M = $(Σ,V,r,T,f)(\Sigma, \bm{V}, \bm{r}, \bm{T}, f)$ , where
a) $Σ={l,r}\Sigma=\{\bm{l},\bm{r}\}$ is the alphabet;
b) $V={v1,…,vn}\bm{V}=\{\bm{v}_1,\ldots,\bm{v}_n\}$ is the set of nodes;
c) $r∈V\bm{r} \in \bm{V}$ is the start node;
d) $ϕ\phi$ is the set of terminal state;
e) f : $V∪{ϕ}×Σ∗→V∪{ϕ}\bm{V}\cup\{\phi\} \times \Sigma^* \to \bm{V}\cup\{\phi\}$ is the transition function.
Any $s∈Σ∗s\in \Sigma^*$ is accepted by the automata iff $st.f(r,s)=v.\forall \bm{v}\in\bm{V},\exists1 \,s∈\Sigma^∗ \,st. f ( r , s ) = v .$

习题3.2 模仿自动机的样子来重新定义树.

A deterministic finite state automata (DFA) is a 5-tuple M = $(Σ,V,r,T,f)(\Sigma, \bm{V}, \bm{r}, \bm{T}, f)$ , where
a) $Σ=N+\Sigma=\bm{N}_+$ is the alphabet;
b) $V={v1,…,vn}\bm{V}=\{\bm{v}_1,\ldots,\bm{v}_n\}$ is the set of nodes;
c) $r∈V\bm{r} \in \bm{V}$ is the start node;
d) $ϕ\phi$ is the set of terminal state;
e) f : $V∪{ϕ}×Σ∗→V∪{ϕ}\bm{V}\cup\{\phi\} \times \Sigma^* \to \bm{V}\cup\{\phi\}$ is the transition function.
Any $s∈Σ∗s\in \Sigma^*$ is accepted by the automata iff $st.f(r,s)=v.\forall \bm{v}\in\bm{V},\exists1 \,s∈\Sigma^∗ \,st. f ( r , s ) = v .$