1. Problem: Write the finite automata corresponding to the regular expression $(a + b)^* ab$. 2. Explanation: The regular expression $(a + b)^* ab$ denotes strings that consist of any combination (including empty) of $a$ and $b$ followed by the substring $ab$ at the end. 3. Construct the automaton: - Start state $q_0$ accepts any string from $(a + b)^*$ by looping on $a$ and $b$. - From $q_0$, when reading $a$, move to state $q_1$ which expects to see $b$ next. - From $q_1$, when reading $b$, move to final state $q_2$ which confirms the substring $ab$ at the end. - $q_2$ is accepting, and no further input is accepted after reaching it. 4. Summary of states and transitions: - $q_0$: start state; loops on $a$, $b$. - $q_1$: transition from $q_0$ on $a$. - $q_2$: transition from $q_1$ on $b$, final accepting state. This forms a deterministic finite automaton (DFA) recognizing $(a + b)^* ab$. Final answer: The finite automaton has states $q_0, q_1, q_2$, with transitions: $$ q_0 \xrightarrow{a} q_1,\ q_0 \xrightarrow{b} q_0,\ q_1 \xrightarrow{b} q_2,\ q_1 \xrightarrow{a} \text{no transition},\ q_2 \text{ is accepting}. $$