## Introduction

A pushdown automaton (PDA) is a computational model that recognizes context-free languages. It consists of an input tape, a stack, and a finite set of states. The PDA transitions between states based on input symbols and stack operations, which allows it to parse and validate strings generated by context-free grammars. In this article, we will discuss pushdown automata in detail.

**A Pushdown Automata (PDA) can be defined as :**

- Q is the set of states
- âˆ‘is the set of input symbols
- Î“ is the set of pushdown symbols (which can be pushed and popped from stack)
- q0 is the initial state
- Z is the initial pushdown symbol (which is initially present in the stack)
- F is the set of final states

Also See, __Moore Machine__

**PDA Components:**

1. Input Tape:

- A read-only tape that contains the input string to be processed by the PDA.

- The input string is a sequence of symbols from the input alphabet.

- The PDA reads the input string from left to right, one symbol at a time.

2. Stack:

- A last-in-first-out (LIFO) data structure used for storing and manipulating symbols.

- The stack has an alphabet of stack symbols, which can be pushed onto or popped from the top of the stack.

- The stack is used to store information and make decisions based on the stored information.

3. States:

- A finite set of states that represent the different configurations of the PDA.

- The PDA transitions between states based on the current input symbol and the top symbol of the stack.

- There is a designated start state where the PDA begins its computation.

- There are also one or more final states (also called accept states) that indicate successful processing of the input string.

4. Transition Function:

- A set of rules that define how the PDA moves from one state to another based on the current input symbol and the top symbol of the stack.

- The transition function specifies the next state, the symbol to be pushed onto the stack (if any), and the symbol to be popped from the stack (if any).

- The transition function can be represented as a transition table or a set of transition rules.

5. Input Alphabet:

- A finite set of symbols that the input string can consist of.

- The input alphabet is used to define the valid symbols that can appear on the input tape.

6. Stack Alphabet:

- A finite set of symbols that can be stored on the stack.

- The stack alphabet includes a special symbol (usually denoted as Z) that represents the bottom of the stack.

7. Acceptance Condition:

- The criteria that determine whether the PDA accepts or rejects an input string.

- The PDA accepts an input string if it reaches a final state after consuming all the input symbols and the stack is empty.

- If the PDA cannot reach a final state or the stack is not empty after consuming all the input symbols, the input string is rejected.