Language Class

Question

Answer 1

a) infinite such no are there to satisty above inequality 
b) in this option also we have one comparison we need stack so CFL but not regular 
c) same as above option we need stack for comparison 
d) this option is regular becaus we have no dependency between m,n,k so it is regular as we can write the regular expression as (a⁺b)⁺a⁺

Comments

i think  c is regular

option D   n,m are unbounded and there is repetation of pattern of a^mb of n times 

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I have one question about the option c ?

would it be regular if {bⁿa^m | m>=n and n <=2009}.

i think it is regular. 

Answer 2

option c is regular language

because n is finite

here total 4020 state is required to construct the dfa

 

just replace 2009 by 3 and then

construct the dfa  it will be easy to understand

Comments

no i don't think so. when traversing through a how will you know the value of n.

I think it will be regular if the power  n is first .

but in the question the power m comes first.