1. **Stating the problem:** We want to understand what a finite automaton is and see an example with a drawing. 2. **Definition:** A finite automaton (FA) is a mathematical model of computation used to recognize patterns or languages. It consists of a finite number of states, transitions between those states based on input symbols, a start state, and one or more accept states. 3. **Components:** - States: Represented as circles. - Alphabet: Set of input symbols. - Transitions: Arrows showing how to move from one state to another based on input. - Start state: Where the automaton begins. - Accept states: States that indicate successful recognition. 4. **Example:** Consider a finite automaton that accepts strings over the alphabet $\{0,1\}$ that end with $1$. 5. **Formal description:** - States: $Q = \{q_0, q_1\}$ - Alphabet: $\Sigma = \{0,1\}$ - Start state: $q_0$ - Accept state: $q_1$ - Transitions: - From $q_0$: on $0$ go to $q_0$, on $1$ go to $q_1$ - From $q_1$: on $0$ go to $q_0$, on $1$ go to $q_1$ 6. **Explanation:** - The automaton starts at $q_0$. - Reading a $1$ moves it to $q_1$, indicating the last read symbol is $1$. - Reading a $0$ moves it back to $q_0$, indicating the last symbol is not $1$. - If the input ends in $q_1$, the string ends with $1$ and is accepted. 7. **Final answer:** The finite automaton described accepts all binary strings ending with $1$.