Lecture Notes on PDA (Pushdown Automata)

Introduction

• Welcome to this video by Geet Smashers.
• Important points of PDA (Pushdown Automata) will be discussed.
• This information will be beneficial for competitive exams and college/university level exams.

Review of Finite Automata

• Finite Automata (DFA, NFA) are used to recognize regular languages.
• Regular languages are powerful, but some languages are more powerful than regular languages.

Example

• Example: 0^n 1^n (where n >= 0)
  • Only 0^n: Can be recognized by Finite Automata.
  • 0^n 1^n: This is more powerful because the number of 0s and 1s must be equal.
  • It requires a comparison, which cannot be done by Finite Automata due to its limited memory.

Need for PDA

• Due to limited memory, extra memory (stack) is needed to compare the number of 0s and 1s.
• Adding a stack to Finite Automata creates a PDA.

Features of PDA

• PDA has push and pop operations.
• For example, put 0 on the stack when it comes and pop 1 when it comes.
• PDA can recognize both regular languages and context-free languages.

Formal Definition of PDA

• PDA is defined using 7 tuples.
  1. Q: Set of finite states
  2. Σ: Set of input symbols
  3. Γ: Set of stack symbols
  4. δ: Transition function
  5. q0: Initial state
  6. Z0: Initial stack symbol
  7. F: Set of final states

Transition Function

• Transition function is based on state, input symbol, and stack symbol.
• Changes can be made to the stack based on input and stack symbols.

Stack Application

• Adding and removing symbols from the stack is possible.
• Z0 is on top of the stack as an initial symbol.
• In the end, if there is a proper transition, the stack can be modified to disappear.

Conclusion

• Further examples will be discussed to understand how the PDA model works.
• Thank you!