Explain the concept of a pushdown automaton.

A pushdown automaton (PDA) is a type of automaton that extends the capabilities of a finite automaton by incorporating a stack. It consists of a finite set of states, an input alphabet, a stack alphabet, a transition function, an initial state, and one or more final states.

The PDA operates by reading input symbols from an input tape and manipulating a stack based on the current state and the input symbol being read. The stack allows the PDA to store and retrieve information, making it more powerful than a finite automaton.

The transition function of a PDA determines the next state and the actions to be performed based on the current state, the input symbol, and the top symbol of the stack. The actions can include pushing a symbol onto the stack, popping a symbol from the stack, or leaving the stack unchanged.

The PDA accepts a given input if, after reading the entire input, it reaches a final state with an empty stack. It can also reject the input if there is no valid transition or if it reaches the end of the input with a non-empty stack.

Pushdown automata are particularly useful in recognizing context-free languages, which cannot be recognized by finite automata alone. They are widely used in various areas of computer science, such as programming language design, parsing, and compiler construction.