Empty State Acceptability
Over reading the input string from the initial for some PDA, the stack of PDA gets empty.
For a PDA, G= (Q, ∑, S, δ, q0, I, F), the language accepted by the empty stack will be as follows:
L(PDA) = {w  (q0, w, I) ⊢* (q, ε, ε), q ∈ Q}
Example 1
We have to construct a PDA that accepts L = { wwR  w = (a+b)* }
Solution
Initially, we will insert a special symbol '$' into the empty stack. At the state q2, the w is being read. Instate q3, each 0 or 1 is popped when it matches the input. The PDA will go into the dead state if any other input is given. When we reach the inserted special symbol '$,' we go to the accepting state q4.
Example 2
We have to construct a PDA that accepts L = {0n 1n  n ≥ 0}
Solution
This language accepts L = {ε, 01, 0011, 000111, ............................. }
In the above example, the number of 'a' and 'b' must be identical.
 Initially, we will insert a special symbol, '$,' in the empty stack.
 At the state q2, if we encounter input 0 and the top is Null, we push 0 into the stack. This may iterate. And if we encounter input 1 and the top is 0, we pop this 0.
 At state q3, by chance, we encounter input 1, and the top is 0. We pop this 0. This may also iterate. And if we encounter input 1 and the top is 0, we pop the top element.

If the special symbol '$' is encountered at the top of the stack, it is popped out, finally going to the accepting state q4.
Also see, Turing Machine in TOC.
Frequently Asked Questions
What type of language is accepted by pushdown automata?
Pushdown automata are used for contextfree languages, i.e., languages in which the length of elements is unrestricted, and one element's length is related to the other.
What are the approaches used by the PDA to accept a language?
Two approaches are using which a language can be accepted.
 Acceptance by final state
 Acceptance by empty stack
What are the types of PushDown automata?
 Decider
 Turing Machine
 Linear Bounded
 Nested stack
 Embedded pushdown
Conclusion
In this blog, we have talked about the following things:
What do you mean by pushdown Automata?
How can a language can be accepted by PDA using the two approaches:
Empty stack acceptability
Final state acceptability
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