Design the minimum-state DFA that accepts all and only the strings of 0’s and 1’s that have 110 as a substring. To verify that you have designed the correct automaton, identify the true statement in a list of choices. These choices will involve:
1. The number of loops (transitions from a state to itself).
2. The number of transitions into a state (including loops) on input 1.
3. The number of transitions into a state (including loops) on input 0.
Count the number of transitions into each of your states (“in-transitions”) on input 1 and also on input 0. Count the number of loops on input 1 and on input 0. Then, find the true statement in the following list.
a) There is one state that has one in-transition on input 0.
b) There is one state that has no in-transition on input 1.
c) There are no states that have two in-transitions on input 1.
d) There is one loop on input 1 and one loop on input 0.