TOC SELF DOUBT

Question

L = { w ∈ {a,b}* : a(w) = b(w) }

We're using the notation:

a(w) = number of a's in a string w
b(w) = number of b's in a string w
S⇾ aSbS | bSaS | ε

 

Doubt:

Is the same language generated by below grammar also:

S⇾ SS | aSb | bSa | ε

Comments

yes both are accepting same language!

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S→ xB ∣ yA

A→ x ∣ xS ∣ yA A

B→ y ∣ yS ∣ xBB

This is also doing the same thing right

Generating strings in which #x's = #y's.