Grammar G = (V N, V T, P, S) –V N : Nonterminal symbols –V T : Terminal symbols V N  V T = , V N ∪ V T = V – P : a finite set of production rules α  β, α ∈ V +, β ∈ V * – S : start symbol(sentence symbol)

Chomsky Hierarchy 생성 규칙 α -> β ∈ P 의 종류에 따라 –Type 0 : No restrictions(unrestricted grammar) –Type 1 : Context-sensitive grammar(CSG).  -> β, |  |  | β| –Type 2 : Context-free grammar(CFG). A -> , where A ∈ V N  S,  ∈ V * –Type 3 : Regular grammar(RG). A -> tB or A -> t, (right-linear) A -> Bt or A -> t, (left-linear) where, A, B ∈ V N  S, t ∈ V T *

Examples –Type 3 : Regular grammar G 1 =({S}, {a, b}, P, S) P: S  aS, S  Sb, S  a, S  b, S   정규식 : a * b * 언어 L(G 1 ) = {a n b m | n  0, m  0} “ aab ” 의 유도 과정 : S  aS (by S  aS)  aaS (by S  aS)  aab (by S  b)

Examples –Type 2 : Context Free Grammar G 2 =({S}, {a, b}, P, S) P: S  aSb, S  ab 정규식 : a n b n 언어 L(G 2 ) = {a n b n | n  1} “ aaabbb ” 의 유도 과정 : S  aSb (by S  aSb)  aaSbb (by S  aSb)  aaabbb (by S  ab)

Examples –Type 1 : Context Sensitive Grammar G 3 =({S,A,C}, {a, b}, P, S) P: S  A, A  abC, bB  bb, A  aABC, CB  BC, bC  bb 정규식 : a n b n 언어 L(G 3 ) = {a n b n | n  1}