Question

.Show a deterministic finite automaton that accepts all binary strings with at least 4 1’s.

2.Show a deterministic finite automaton that accepts all binary strings with a number of 1’s divisible by 3.

Answer 1

To construct a deterministic finite automaton (DFA) that accepts all binary strings with at least 4 1's, create states representing different possibilities of having 1's in the string and designate states with at least 4 1's as accepting states. To construct a DFA that accepts all binary strings with a number of 1's divisible by 3, follow a similar process but designate states with a number of 1's divisible by 3 as accepting states.

Step-by-step explanation:

To construct a deterministic finite automaton (DFA) that accepts all binary strings with at least 4 1's, you can follow these steps:

1. Create states that represent different possibilities of having 1's in the string. For example, one state can represent no 1's, another state can represent 1's, and so on.
2. Label the transitions from one state to another with 0 or 1, depending on whether the input symbol is 0 or 1.
3. Designate one of the states as the start state and mark certain states as accepting states. In this case, mark the states with at least 4 1's as accepting states.
4. Ensure that from each state, there is a transition for both 0 and 1.

To construct a DFA that accepts all binary strings with a number of 1's divisible by 3, follow a similar process:

1. Create states that represent different possibilities of having a number of 1's divisible by 3.
2. Label the transitions from one state to another with 0 or 1, depending on whether the input symbol is 0 or 1.
3. Designate one of the states as the start state and mark certain states as accepting states. In this case, mark the states with a number of 1's divisible by 3 as accepting states.
4. Ensure that from each state, there is a transition for both 0 and 1.