Grammar Introduction
Chomsky establish formal language system in 1956, he put grammar into four types: type 0,1,2,3
Type 0
The phrase grammar, Turing machine
- Production of the form:
$$
\alpha \rightarrow \beta
$$
- among them:
$$
\ Alpha \ in (V_T \ V_n Cup) and having at least one nonterminal Beta \\ \ in (V_T \ Cup V_n)
$$
Type 1
Context-sensitive grammar, linear boundaries automaton
- Production of the form:
$$
\alpha \rightarrow \beta
$$
- among them:
$$
|\alpha|\le|\beta|,仅S \rightarrow \epsilon
$$
Type 1 generation grammar all left-hand side may contain one, two or more characters, but must have at least a nonterminal
Type 2
Context-free grammar, non-deterministic pushdown automaton
- Production of the form:
$$
A \rightarrow \beta
$$
- among them:
$$
A \in V_N; \space \beta \in (V_T \cup V_N)*
$$
Type 3
Formal grammars, finite automata
Right Linear Grammar
- Production of the form:
$$
A\rightarrow \alpha B \space或 A \rightarrow \alpha
$$
- among them:
$$
\alpha \in V_T*; \space A,B \in V_N
$$
Left linear grammar
- Production of the form:
$$
A \rightarrow B \alpha \space 或 A \rightarrow \alpha
$$
- among them:
$$
\alpha \in V_T*; \space A,B \in V_N
$$