Pushdown_Automata_Presentation in Automata theory and compiler design

1. Pushdown Automata (PDA)
• A detailed overview of concepts, structure,
and applications
• Presented by: [Your Name]

2. Introduction to PDA
• - Pushdown Automata (PDA) is a type of
automaton that employs a stack.
• - It extends the capability of Finite Automata
by using a stack memory.
• - Used to recognize Context-Free Languages
(CFLs).

3. Why PDA?
• - Finite Automata cannot handle nested
structures (like parentheses).
• - PDA is capable of handling such recursive
patterns due to its stack.
• - Example: Recognizing strings like a^n b^n.

4. Formal Definition
• A PDA is defined as a 7-tuple:
• M = (Q, Σ, Γ, δ, q0, Z0, F), where:
• Q: Finite set of states
• Σ: Input alphabet
• Γ: Stack alphabet
• δ: Transition function
• q0: Start state
• Z0: Initial stack symbol
• F: Set of accepting states

5. PDA Transitions
• A transition is of the form:
• δ(q, a, X) = {(p, γ)}
• - q: current state
• - a: input symbol (or ε)
• - X: top of the stack
• - p: next state
• - γ: string to replace X on stack

6. Types of Acceptance
• - PDA can accept input in two ways:
• 1. Acceptance by Final State
• 2. Acceptance by Empty Stack
• - Both types are equivalent in terms of the
class of languages they recognize.

7. Instantaneous Description (ID)
• An ID is a snapshot of PDA:
• (q, w, γ)
• - q: current state
• - w: unread input
• - γ: current stack contents
• Example: (q0, abb, Z0)

8. Designing PDA – General Approach
• 1. Understand the language
• 2. Design transitions based on stack behavior
• 3. Handle inputs and matching stack
operations
• 4. Define accepting condition (final state or
empty stack)

9. Example: L = { a^n b^n | n ≥ 0 }
• 1. Push 'a' onto stack for each 'a' in input.
• 2. For each 'b', pop 'a' from stack.
• 3. Accept when input ends and stack has initial
symbol.

10. Example: PDA for Palindromes
• - Input: Palindromes like 'abba', 'abcba'
• - Strategy:
• 1. Push first half onto stack
• 2. Skip middle if odd length
• 3. Match and pop second half

11. Deterministic vs Non-deterministic
PDA
• - Deterministic PDA (DPDA):
• * At most one possible move for a given
input and stack
• - Non-deterministic PDA (NPDA):
• * Multiple possible transitions
• * More powerful than DPDA

12. Applications of PDA
• - Syntax analysis in compilers
• - Parsing of programming languages
• - Recognizing nested structures like
parentheses
• - Model for context-free grammar (CFG)
evaluation

13. Limitations of PDA
• - Cannot recognize context-sensitive or
recursive languages
• - Stack allows only limited memory access
(LIFO)
• - Less powerful than Turing Machines

14. PDA vs Other Automata
• | Feature | Finite Automata | PDA | Turing
Machine |
• |---------|------------------|-----|----------------|
• | Memory | None | Stack | Infinite tape
|
• | Language | Regular | CFL | Recursively
enumerable |
• | Power | Limited | Moderate | Most
powerful |

15. Summary
• - PDA = Finite Automaton + Stack
• - Useful for recognizing Context-Free
Languages
• - Important in theoretical computer science
and compilers

16. Q&A
• Thank you!
• Questions are welcome.