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A Pushdown Automaton (PDA) is a type of automaton used in theoretical computer science to recognize context-free languages. PDAs are similar to finite automata (FAs) but with the addition of a stack, which provides them with more computational power.

Components of a PDA:

  1. Input Tape: Similar to finite automata, a PDA has an input tape containing a string of symbols from the input alphabet.
  2. Control Unit: The control unit is responsible for reading symbols from the input tape and determining transitions between states based on the current input symbol and the top symbol of the stack.
  3. Stack: The stack is a last-in, first-out (LIFO) data structure that stores symbols. The stack provides the PDA with memory, allowing it to recognize non-regular languages. The PDA can push symbols onto the stack, pop symbols from the stack, or inspect the top symbol of the stack without removing it.


The transition function of a PDA determines how the PDA moves from one configuration to another based on the current input symbol and the top symbol of the stack. A transition is represented as:

δ(q, a, X) = { (p, β) }


  • q is the current state
  • a is the current input symbol
  • X is the top symbol of the stack
  • p is the next state
  • β is a string representing the symbols to push onto the stack (or ε if no symbols are pushed)


  1. The PDA starts in a designated start state with an empty stack.
  2. It reads symbols from the input tape one at a time, along with the top symbol of the stack.
  3. Based on the current state, input symbol, and top stack symbol, the PDA follows transitions to move to the next state and manipulate the stack.
  4. If the PDA reaches an accept state and the input tape is empty, the input string is accepted. Otherwise, it is rejected.

Acceptance Criteria:

A PDA accepts a string if it can reach an accept state with an empty input tape. The PDA may or may not have symbols remaining on the stack when it reaches an accept state.


  1. Parsing: PDAs are used in parsing algorithms to analyze the syntactic structure of programming languages or other formal languages.
  2. Compiler Construction: PDAs are used in lexical analysis and syntax analysis phases of compiler construction.
  3. Natural Language Processing: PDAs can be used to model and analyze the structure of natural languages.

Overall, PDAs are a fundamental concept in formal language theory and computational theory, providing a theoretical framework for understanding the computational complexity of context-free languages.