DCFL or CFL ?

Question

L = {$a^{n+m}b^{n}a^{m} | n,m \geq 0$}

Is the above language DCFL or CFL ?

Answer 1

The language is both DCFL and CFL. Even every DCFL is CFL.

[ DCFL → Deterministic Context Free Language, CFL → Context Free Language ]

We can design deterministic push-down automata for the above language.

Logic: Start reading i/p →  Push all the a’s inside the stack → on seeing b’s start popping a’s from the stack top →   on seeing a’s start popping a’s from the stack top → If the input string ended and no i/p symbol(a’s) left inside the stack then accept the string else reject.

Comments

if n=0 then how will we know when to start popping a’s as there will be no ‘b’ present in middle to differentiate.

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@Abhrajyoti00  check this one.

Answer 2

for MSQ go with CFL AND DCFL.

But For MCQ go With DCFL.

As far as my Knowledge