Find dfa’s that accept the following languages:(a) L (aa∗ + aba∗b∗).

Sure, I can help with that. Here's how you can construct DFA's for the given languages:

(a) L (aa* + abab)

Step 1: Define the Alphabet The alphabet for this language is {a, b}.

Step 2: Define the States We'll need several states to recognize the different parts of the language. Let's call them:

• S0: The start state
• S1: Recognizes 'a'
• S2: Recognizes 'aa*'
• S3: Recognizes 'ab'
• S4: Recognizes 'aba*'
• S5: Recognizes 'abab'

Step 3: Define the Transition Function The transition function δ is defined as follows:

• δ(S0, a) = S1
• δ(S1, a) = S2
• δ(S2, a) = S2
• δ(S1, b) = S3
• δ(S3, a) = S4
• δ(S4, a) = S4
• δ(S4, b) = S5
• δ(S5, b) = S5

All other transitions lead to a dead state.

Step 4: Define the Start State The start state is S0.

Step 5: Define the Accept States The accept states are S2, S4, and S5. These states represent the successful recognition of the strings 'aa*', 'aba*', and 'abab', respectively.

This DFA recognizes the language L (aa* + abab).