1. Context Free Grammar: Simplification
Erwin Yudi Hidayat

2. CFG Simplification
Purpose: to limit or minimize complexity in parsing a tree due to unnecessary production rule
Example: production rule in CFG is defined as follow:
SAB  a
Aa
???

3. CFG Simplification
Purpose: to limit or minimize complexity in parsing a tree due to unnecessary production rule
Example: production rule in CFG is defined as follow:
SAB  a
Aa
B has no derivation...

4. D  A : causes complexity (redundant)
CFG Simplification
What about this one?
SA
AB
BC
CD
Da  A
Lengthy path
D  A : causes complexity (redundant)

5. CFG Simplification Context Free Grammar can be simplified by:
Useless production elimination
Unit production elimination
 production elimination

6. Useless Production Elimination
Useless production is defined as:
Any production contains variable which has no derivation to produce terminals. This production is useless as endless derivation (variable symbol still remains)
Any production that never can be reached using any derivation from start symbol, therefore this production is redundant.

7. Useless Production Elimination
Example: production rule in CFG is as follow:
SaSa Abd  Bde
AAda
BBBB  a
Variable A has no derivation to reach terminal
As consequence, S Abd has no derivation
Simplified CFG:
SaSa  Bde

8. Useless Production Elimination
Example: production rule in CFG is as follow:
S Aa  B Aab  D
Bb  E Cbb
EaEa
Variable E has no derivation to reach terminal
Variable D has no derivation to reach terminal
Variable C never be used
Simplified CFG: SAa  B
Aab
Bb

9. Unit Production Elimination
Unit production is defined as any production that consist only one single variable symbol, e.g. A B, C  D
Example: production rule in CFG is as follow:
SSb
SC
CD
Cef
Ddd

10. Unit Production Elimination
Unit production is defined as any production that consist only one single variable symbol, e.g. A B, C  D
Example: production rule in CFG is as follow:
SSb
SC
CD
Cef
Ddd

11. Unit Production Elimination
Unit production is defined as any production that consist only one single variable symbol, e.g. A B, C  D
Example: production rule in CFG is as follow:
SSb
SC
Cdd
Cef
Ddd

12. Unit Production Elimination
Unit production is defined as any production that consist only one single variable symbol, e.g. A B, C  D
Example: production rule in CFG is as follow:
SSb
SC
Cdd
Cef
Ddd

13. Unit Production Elimination
Unit production is defined as any production that consist only one single variable symbol, e.g. A B, C  D
Example: production rule in CFG is as follow:
SSb
Sdd | ef
Cdd
Cef
Ddd

14. Unit Production Elimination
Unit production is defined as any production that consist only one single variable symbol, e.g. A B, C  D
Example: production rule after simplification:
SSb
Sdd | ef
Cdd
Cef
Ddd

15. Unit Production Elimination
Ctd...