PDA examples help you understand how Pushdown Automata recognize context-free languages. Pushdown Automata (PDA in TOC) is an important topic in Theory of Automata and is widely asked in exams like GATE, NTS, and university finals.
In this SEO-optimized article, you will learn PDA examples in simple wording with clear explanations.
What is a Pushdown Automaton (PDA)?
A Pushdown Automaton (PDA) is a computational model that:
- Reads input symbols
- Changes states
- Uses a stack (memory)
- Accepts or rejects strings
A PDA is more powerful than a Finite Automaton because it can use a stack.
Basic Structure of PDA
A PDA consists of:
- Set of states (Q)
- Input alphabet (Σ)
- Stack alphabet (Γ)
- Transition function (δ)
- Start state (q₀)
- Stack start symbol (Z₀)
- Final states (F)
Example 1: PDA for L = { aⁿbⁿ | n ≥ 0 }
This is the most common PDA example.
Language Meaning:
- Equal number of a’s and b’s
- All a’s come first
- Then all b’s
Valid strings:
- ε
- ab
- aabb
- aaabbb
Idea of Solution
- Push each a into the stack
- For every b, pop one a
- Accept if stack becomes empty
PDA Working Steps
Step 1:
On reading a → push A into stack
Step 2:
On reading b → pop A from stack
Step 3:
If input ends and stack is empty → Accept
Transition Explanation
- δ(q₀, a, Z₀) → (q₀, AZ₀)
- δ(q₀, a, A) → (q₀, AA)
- δ(q₀, b, A) → (q₁, ε)
- δ(q₁, b, A) → (q₁, ε)
Accept when stack becomes Z₀ and input is empty.
Example 2: PDA for L = { aⁿb²ⁿ | n ≥ 0 }
Language Meaning:
- For every 1 “a”, there must be 2 “b”
Valid strings:
- ε
- abb
- aabbbb
- aaabbbbbb
Idea of Solution
- Push two symbols for each “a”
- Pop one symbol for each “b”
- Accept if stack becomes empty
This ensures:
Number of b’s = 2 × number of a’s
Example 3: PDA for Palindrome Language
Language:
L = { wwᴿ | w ∈ {a, b}* }
Example strings:
- aa
- bb
- aba
- abba
Idea of Solution
- Push first half of string into stack
- Compare second half by popping
- Accept if matched
This requires guessing middle point (non-deterministic PDA).
PDA Acceptance Methods
There are two ways PDA accepts a string:
1️⃣ Acceptance by Final State
String is accepted if PDA reaches a final state.
2️⃣ Acceptance by Empty Stack
String is accepted if stack becomes empty.
Both methods are equivalent in power.
Why PDA is Important?
Pushdown Automata:
- Recognize Context-Free Languages
- Used in compiler parsing
- Help understand syntax analysis
- Important for Theory of Automata exams
Difference Between FA and PDA
| Feature | FA | PDA |
| Memory | No memory | Stack |
| Language Type | Regular | Context-Free |
| Power | Less | More |
Real-Life Application of PDA
- Programming language parsing
- Syntax checking
- Expression evaluation
- Grammar checking systems
Conclusion
PDA examples help us understand how stack-based machines work. A Pushdown Automaton can recognize languages that Finite Automata cannot, such as:
L = { aⁿbⁿ | n ≥ 0 }
By mastering PDA examples, you strengthen your understanding of Context-Free Languages and Compiler Design concepts.