Question

Give the state diagrams of NFAs with the specified number of states recognizing the following languages over = {0, 1}:

a. Lø with one state
b. Lę with one state
c. {w: w contains only 0’s}with one state

Answer 1

State diagrams for NFAs recognizing Lø, Lε, and the language of strings containing only 0's with one state are a non-accepting state with no transitions, an accepting state with no transitions, and an accepting state with transitions on '0' to itself, respectively. The correct multiple-choice option is (b).

Step-by-step explanation:

When creating state diagrams for non-deterministic finite automata (NFAs) that recognize specific languages over the alphabet {0, 1}, we consider the simplest cases with only one state:

• Lø (the empty language): This NFA will have one state, which is not an accepting state. There will be no transitions since this automaton accepts no strings, not even the empty string.
• Lε (the language containing only the empty string ε): This NFA will also have just one state, which is an accepting state. There will be no transitions from this state, but it accepts the empty string because the initial state is also the accepting state.
• {w: w contains only 0’s}: This NFA will have one state which is an accepting state. There will be a transition from this state to itself on input '0' to accept strings of arbitrary length containing only the digit '0'. There are no transitions on '1' to ensure that strings containing '1' are not accepted.

The state diagrams for NFAs are essential in theoretical computer science and automata theory as they visually represent how an automaton processes input strings to determine membership in the specified language. The correct multiple-choice option is (b).