Type 0 grammar
- Set = G (V N , V T , P, S) is a grammar, if each of its production α → β is a structure: ae (V N ∪ V T ) * and containing at least one non-terminal Fu , while β∈ (V N ∪ V T ) * , then G is a 0-type grammar
- Also known phrase grammar, ability to type 0 grammar is equivalent to a Turing machine (Turing machine); any type 0 languages are recursively enumerable ; on the contrary, must be recursively enumerable set a language 0
Type 1 or context sensitive (context-sensitive)
- Setting G = (V N , V T , P, S) is a grammar, if each of P in the production α → β both satisfying | β | ≥ | α | except only S → [epsilon] , then the grammar G is 1 type or context-related
- In some definitions, the form of context-sensitive grammar productions described as [alpha] . 1 Aa 2 → [alpha] . 1 βα 2 , wherein [alpha] . 1 , [alpha] 2 and beta] are (V N ∪ V T ) * beta] ≠ [epsilon], A in V N
- Better reflect the "context-sensitive" because only A occurs in the [alpha] . 1 and [alpha] 2 context of , allowed substituted with A β
Type 2 or contextual (context-free)
- Set = G (V N , V T , P, S) is a grammar, if P in each of the production α → β satisfy the [alpha] is a terminator , β∈ (V N ∪ V T ) * , grammars G is a type 2 or a context-free
- 2 indicating the type sometimes generative grammar in the form A → β, where A∈V N , i.e., when substituted with nonterminal beta] A, where A is independent of the context, the context is irrelevant named
Example 2.4 G = ({S, A, B}, {a, b}, P, S), where P is generated by the following composition formula:
- S→aB
- A→aAA
- S→bA
- B→b
- A→a
- B→bS
- A→aS
- B→aBB
Can produce the same type of a left portion, abbreviated as [alpha] → A . 1 | [alpha] 2 | ... | [alpha] n- , the pivot symbol | pronounced "or"
2.4 examples of P can be written as
- S → aB | bA
- A → a | aS | Bar
- B → b | AA | aBB
Type 3 grammar or regular grammar
Set = G (V N , V T , P, S), if the production of each of the form P is A → aB or A → a, wherein A and B are nonterminals, a∈V * T , G is the type 3 grammar or regular grammar
Example 2.5 grammar G = ({S, A, B}, {0,1}, P, S), where P is generated by the following composition formula:
- S→0A
- S→1B
- S→0
- S→0
- A→0A
- A→1B
- B→1B
- B→1
- B→0
G is a regular grammar