Study Notes on Closure properties of Languages

By Mukesh Kumar|Updated : December 1st, 2021

Closure properties on regular languages are defined as certain operations on regular language which are guaranteed to produce regular language. Closure refers to some operation on a language, resulting in a new language that is of the same “type” as originally operated on i.e., regular.

The table below shows the closure properties of all the formal languages. 


Note :Union , Intersection or difference with regular doesn't change the language. i.e.

Let (AnyLANG) below represents any of the language among DCFl , CFl , CSL , RE or REC

Regular ∩ AnyLANG = AnyLANG

Regular ∪ AnyLANG = AnyLANG

Regular - AnyLANG = AnyLANG 

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Mukesh KumarMukesh KumarMember since Feb 2020
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BhushanJan 26, 2017

How we used this chart in problem solving please share...
Rachakonda Manasa
Sir in cs I would like to study java,python n etc.So i can do cs engeering or i should  refer to degree college
Pallavi Choudhary
@Mallesham Devasane Hi Sir,
DCFL is not closed under reversal.Request you to please verify and correct the table.
I generally refer grade up notes a lot and hence please verify if the decidability chart is also correct.
...Read More
Sudipta Dhar
Kindly mention how the chart is working.
I cannot understand with whom the union intersection etc operations are working

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