self-doubt

Question

1-can a language L & L^R  be equal in any case ? if they are when?

2- if L={0^m1ⁿ | m,n$\geq$0}  and 

L^R={1^m0ⁿ | m,n$\geq$0}   are two language then are they equal?

Comments

can a language L & L^R  be equal in any case ? if they are when?

yes.

L = { W.W^R  | W ∈ (0+1)* }  ===> collection of palindrome strings.

---

---

 L={0^m1ⁿ | m,n≥0}  and  L^R={1^m0ⁿ | m,n≥0}   are two language then are they equal?

 L = {∈,0, 00,000,...... 1,11,111,1111,....... 01,001,0001,.....}

L^R = {∈, 0,00,000,..... 1,11,111,1111,...... 10,110,.......}

those are not equal.

---

let L=a*, then its reversal is also the same language

in ur case L=0^m1^m .....any number of zeros followed by any number of ones

L={01,0011,000111..........}

if you reverse it then

L^R ={10,1100,111000........}

clearly they are not equal

---

thanks

Answer 1

 L={0m1n | m,n≥0} for these the language generated is L={E,0,1,01,001,0011....}  --> so it will never contain 10,1100..in these 0 will never come after 1,

But in L^R={1^m0ⁿ | m,n≥≥0} for these the language generated is L={E,0,1,10,100,1100....}--->so it will never contain 01,0011..in these 1 will never come after 0.