Question

While proving Inverse Homomorphism, which of the following steps are needed?

(a) Start with a DFA Ain L

(b) Construct a DFA B for h-1(L)

(c) The set of states, initial and final states should be same.

(d) All of the mentioned

This question was posed to me during an online exam.

The question is from Reversal-Homomorphism and Inverse Homomorphism topic in section Properties of Regular Languages of Automata Theory

Answer 1

The correct choice is (d) All of the mentioned

Explanation: While constructing DFA B, we need to take care of the following:

a) The same set of states

b) The same start state

c) The same final state

d) Input alphabet = the symbols to which homomorphism h applies.