I've spend the last few days searching online for an example of a constructive proof of regular languages being closed under homomorphism, but I have not seen one. I am mostly unsure of how to show the construction of a DFA for a homomorphism in general. For example, if I were to create a mapping between an alphabet $A$ and the binary alphabet $B$, how would I go about showing the construction of a DFA to recognize this mapping? I would really appreciate any help, whether with an actual example, or just an idea of what I would need to do.
Writing a constructive proof for closure of a regular language under homomorphism
regular languages;proof techniques;closure properties