GATE CSE 1992 | Question: 02,xix

Question

Context-free languages are:

• A. closed under union
• B. closed under complementation
• C. closed under intersection
• D. closed under Kleene closure
   

Answer 1

Answer: A;D.

Context-Free languages are not closed under intersection and complementation.

Comments

CFG are closed under Union , Kleen closure & Concatenation .

Also CFG are closed under Regular intersection

BUT , are CFG closed under Regular Union ?

I think yes...coz..every regular is CFG & CFG are closed under union ....

correct me if I am wrong

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So take two regular language sigma* over {a,b} and other as {a}then their union is sigma* ,which is not cf.

Correct me if I am wrong.

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https://gateoverflow.in/?qa=blob&qa_blobid=8929616163903734815

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@air1ankit I have some doubt in the above table
 

       1. DCFL closed under reversal?

2. CSL closed under set difference?
3. REC under epsilon free substitution?

for 1. formal languages - Are DCFLs closed under reversal? - Computer Science Stack Exchange 

Answer 2

According to the above table we can say , A and D is correct answer

Comments

wat is GSM mapping ??

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Gsm mapping Short for generalized sequential machine mapping. A function that is the response function of a generalized sequential machine, and therefore generalizes the notion of sequential function. Without constraining the machine to have a finite state-set, generalized sequentiality is equivalent to the following property of initial subwords preservation: 

for all u,v in I*, f(uv) has the form f(u)w for some w in O*, where I* and O* are the sets of all input and output strings.

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What is Substitution Operation?

Answer 3

A is right

D is right because

$(CFL)^* = Regular$

all regular are CFL’s

Comments

From where did you get  that $(CFL)^*$ = Regular?

Answer 4

A & D

CFL’s are NOT CLOSED under INTERSECTION, COMPLEMENTATION, DIFFERENCE.

DCFS’s are NOT CLOSED under INTERSECTION, UNION, CONCATENATION, KLEENE CLOSURE, DIFFERENCE, REVERSAL, HOMOMORPHISM.