Simplifications Context-Free Grammars - WPI
Simplifications of
Context-Free Grammars
Fall 2004
COMP 335
1
A Substitution Rule
S aB A aaA A abBc B aA Bb
Substitute
Bb
Fall 2004
COMP 335
Equivalent grammar
S aB | ab A aaA A abBc | abbc B aA
2
A Substitution Rule
S aB | ab A aaA A abBc | abbc B aA
Substitute
B aA
Fall 2004
S aB | ab | aaA A aaA A abBc | abbc | abaAc
COMP 335
Equivalent grammar
3
In general:
A xBz
B y1
Substitute
B y1
A xBz | xy1z
equivalent grammar
Fall 2004
COMP 335
4
Nullable Variables
- production :
A
Nullable Variable:
AK
Fall 2004
COMP 335
5
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