Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
What are the closure properties for context free language?
The closure properties for context free language (CFG) are as follows −
Closed under Union Operation
n order to show that context-free language is closed under union operation, consider two starting variables S1 and S2 for the two different languages L1 and L2.
Grammar for union operation is as shown below −
S ->S1|S2
If both the languages belong to the context free language then union of both the languages should belong to context free language.
By the above definition if a user generates S1 and S2 string or both then in that case union of both the language is generated.
Hence, L1 U L2 ∈ CFL
So, context free language is closed under union operation.
Closed under Concatenation
In order to show that context free language is closed under concatenation, the operation considers two starting variables S1 and for the two different languages L1 and L2.
Grammar for union operation is as shown below −
S->S1S2−
If both the language belongs to the context free language then concatenate one of both the language should belong to context free language.
∀L1L2∈CFL
{W1W2:W1∈L1∈ΛW2∈L2}∈CFL
By the above definition if a user generates S1 string for language L1 followed by S2 string of language. Then, its concatenation of both languages is generated.
Hence, the result is as follows −
{W1W2:W1∈L1∈ΛW2∈L2}∈CFL
So, context free language is closed under concatenation operation.
Closed under Star operation
In order to show that context free language is closed under star operation. Consider one start variable S1 for the languages L1
Grammar for union operation is as shown below −
S->S1S| ∈
If the language belongs to the context free language then the star of the language should belong to the context free language.
∀L1∈CFL
By the above definition, if the user generates zero or many strings which is the definition of the star. So, context free language is closed under star operation.
4K+ Views
To Continue Learning Please Login