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1 The Cocke-Younger-Kasami Algorithm * Chung, Sei Kwang *Alfred Aho, Jeffrey Ullman 의 “The Theory of Parsing, Translation, and Compiling” 과 인터넷을 참고하여 작성되었습니다.

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Presentation on theme: "1 The Cocke-Younger-Kasami Algorithm * Chung, Sei Kwang *Alfred Aho, Jeffrey Ullman 의 “The Theory of Parsing, Translation, and Compiling” 과 인터넷을 참고하여 작성되었습니다."— Presentation transcript:

1 1 The Cocke-Younger-Kasami Algorithm * Chung, Sei Kwang *Alfred Aho, Jeffrey Ullman 의 “The Theory of Parsing, Translation, and Compiling” 과 인터넷을 참고하여 작성되었습니다.

2 2 Contents Preliminaries  Context Free Grammar  Chomsky Normal Form  Dynamic Programming CYK algorithm  Purpose of parsing  Premise  Constructing the parse table  Left parsing from the parse table

3 3 Preliminaries(1) Context Free Grammar(1)  Grammar  Notation ; G = (N, Σ, P, S)  N ; a finite set of non-terminal symbols  Σ ; a finite set of terminal symbols  P ; a finite subset of (N ∪ Σ)*N(N ∪ Σ)*×(N ∪ Production : (α, β) ∈ P will be written α → β  S ; the start symbol in N

4 4 Preliminaries(2) Context Free Grammar(2)  CFG  G ; if each production in P is of the form A → α, where A is in N and α is in (N ∪ Σ)* Chomsky Normal Form  Production can be 1 of 2 formats  A → α  A → e – production ; ex) 00A1 → 001 ( ∵ A → e ∈ P )

5 5 Preliminaries(3) Dynamic Programming  Optimal substructure  Solution of problem = Σ Solution of subproblem  Overlapping subproblem  X = S1 + S2  S1 = T1 + T2 + T3  S2 = T2 + T3 + T4  T2, T3 overlapped  Recording solutions to reduce calculation  Reuse the recorded solutions

6 6 CYK algorithm(1) Premise  G = (N, Σ, P, S) ; a Chomsky normal form CFG with no e-production  The input string w = a 1 a 2 …a n  Each a i ∈ Σ (1≤i ≤n)  The element of the parse table, T ; t ij Purpose of parsing  To determine whether string w is in L(G)  Input string w is in L(G) ⇔ S is in t 1n

7 7 CYK algorithm(2) Constructing the parse table(1)  Input ; w = a 1 a 2 …a n ∈ Σ+  Output ; The parse table T for w such that t ij contains A ⇔ A + ⇒ a i a i+1 …a i+j-1  Method  1 st, t i1 = {A|A→a i ∈ P, 1≤i≤n}  2 nd, 1≤k

8 8 CYK algorithm(3) Constructing the parse table(2)  Example  Input string; abaab(n=5)  Productions;  S→AA|AS|b  A→SA|AS|a Parse table → 5A,S 4 3 S 2 AS 1ASAAS jiji 12345

9 9 CYK algorithm(4) Left parsing from the parse table(1)  Input ;  A Chomsky normal form CFG G = (N, Σ, P, S)  Numbered productions  Input string w  The parse table  Output ;  a left parse for w or the signal “error”

10 10 CYK algorithm(5) Left parsing from the parse table(2)  Method ; A recursive routine gen(i,j,A); generate a left parse corresoding to the derivation A + ⇒ a i a i+1 …a i+j-1  1 st, if j = 1, the mth production in P is A→a i then output m  2 nd, if j > 1, k(1≤k

11 11 CYK algorithm(6) Left parsing from the parse table(3)  Example  Input ;  w = abaab  Numbered productions  1. S → AA  2. S → AS  3. S → b  4. A → SA  5. A → AS  6. A → a  Output ;  : S → AA 6: A → a 4: A → SA 3: S → b 5: A → AS 6: A → a 2: S → AS 6: A → a 3: S → b 5A,S 4 3 S 2 AS 1ASAAS jiji 12345

12 12 Thank you for listening. 경청해주셔서 감사합니다. 설은 가족과 함께 행복하게 보내세요.


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