# Design a pushdown automaton recognizing L={a^nb^m∣n≥m≥0}

## Final answer:

**A pushdown automaton** can be used to recognize the language L={a^nb^m∣n≥m≥0}.

## Explanation:

**A pushdown automaton** is a type of finite automaton that uses a stack to store and retrieve information. To design a pushdown automaton recognizing the language L={a^nb^m∣n≥m≥0}, we can use three states:

**State 1:** Read 'a' and push it onto the stack. Transition to State 2.

**State 2:** Read 'a' and push it onto the stack. Transition to State 2.

**State 2:** Read 'b' and pop 'a' from the stack. Transition to State 3.

**State 3:** Read 'b' and pop 'a' from the stack. Transition to State 3.

**State 3:** If we reach the end of the input string and the stack is empty, accept the input. Otherwise, reject the input.

This pushdown automaton recognizes strings where the number of 'a's is greater than or equal to the number of 'b's. For example, it will accept 'aabb' but reject 'aabba'.

What is the key feature of a pushdown automaton? The key feature of a pushdown automaton is its ability to use a stack to store and retrieve information, allowing it to recognize context-free languages.