REGULAR OR NOT

Question

WHICH ONE REGULAR 

1.{a^m b^n} m=4-n

2{a^m b^n} m=n-4

3.{a^m b^n} m-n=4

Answer 1

$L_1=\{a^mb^n \; \mid m=4-n\}$

$L_1$ can be written as 

$L_1=\{a^mb^n \; \mid m+n=4\} $  is regular, having regular expression $a^4+a^3b+a^2b^2+ab^3+b^4$ 

$L_2=\{a^mb^n \; \mid m=n-4\}$

$L_2$ can be written as 

$L_2=\{a^mb^n \; \mid n=m+4\}$ 

or, $L_2=\{a^mb^{m+4} \}=\{a^mb^mb^4 \}$ is CFL

$L_3=\{a^mb^n \; \mid m-n=4\}$

$L_3$ can be written as 

$L_3=\{a^mb^n \; \mid m=n+4\}$

or, $L_3=\{a^{n+4}b^n \}= \{a^4a^nb^n\}$ is CFL