what is the left quotient of a CFL with a regular language ?

Question

If I take L=a^n b^n and R=(a+b)* so I am getting the value of L/R to be regular ,Am I correct ?

Answer 1

I think ans will be (B)

B is a part of xy , as y∊B

xy∊ A , 

now L/R (or A/B or xy/y)

=CFL / regular

let CFL =aⁿbⁿ

regular= b⁴

So, L/R= aⁿb^n-4 

which is also CFL

Comments

yes

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@Arjun Sir ,In question x=Σ*, question is having a definition of right quotient how we have conclude left quotient ,

(there exist)y∊B and xy∊A

A/B

sorry i know i am wrong , but not getting how it is left quotient?

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cfl/phi operation will be undefined. rightR?

Answer 2

CFL NEED NOT REGULAR.

1.for the taken example take R=b*

then L/R = a* (n>=0) which is regular.

2. take R=b^10

then L/R = a^n b^n-10, which CFL but not regular.

hope this will help.

Comments

sorry but the quotient doesn’t work like you’ve mentioned.

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It's mentioned in question, correspondingly i made an example.

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oh yes, I am sorry. Because of syntax, I interpreted it wrongly.