How to construct a DFA?
Could you elaborate on the process of constructing a Deterministic Finite Automaton (DFA)? What are the key steps involved in designing a DFA for a given language? What considerations should be taken into account while defining the states and transitions? Additionally, how do you ensure that the DFA is minimal, meaning it has the least number of states possible for the given language? Also, how do you handle epsilon transitions, if any, in the DFA? Lastly, could you provide an example of a DFA for a simple language, such as the language of all strings ending with 'ab', to demonstrate the construction process?