Theoretical Approach for Deterministic Finite Automata

Question

Let L be a language accepted by a DFA. Let L ́ be the language obtained by deleting the last symbol of every string of L. Find out if it is possible to construct a DFA accepting L ́.

How to approach this particular problem ?

A probable solution can be (my approach) by making just the preceding state of the final state as the final state and omit the old final states. Is it correct ??

Answer 1

Your approach has 2 problems: there is not a unique preceding state, there can be a lot and if you make them final (if they aren't) you are most of the time perturbating the initial language and adding some extra words to it. But you're on the right track. The solution is to remove the last state, and add a new final state with epsilon-transitions from all preceding states to the new final state.