Question

Give state diagrams of NFAs with the specified number of states recognizing each of the following languages. In all parts the alphabet is {0,1}.

a. The language {w] w ends with 00} with three states
b. The language of Exercise 1.6c with five states
c. The language of Exercise 1.61 with six states
d. The language {0} with two states
e. The language 0*1*0* with three states A
f. The language 1*(001*)* with three states
g. The language {e} with one state
h. The language 0* with one state

Answer 1

a. The language w ends with 00 with three states:

The student's question pertains to creating state diagrams of Non-deterministic Finite Automata (NFAs) for various specified languages over the alphabet {0,1}, with constraints on the number of states.

Step-by-step explanation:

The student is asking for state diagrams of Non-deterministic Finite Automata (NFAs) for specific languages over the alphabet {0,1}. NFAs are abstract machines used in computer science to recognize patterns of input.

They can transition to any number of states for each alphabet symbol, which includes making transitions without consuming any input known as ε-transitions, and can be in multiple states at once.

For instance, for the language of strings ending with "00" with three states, the NFA would begin in an initial state that transitions to itself on both "00" and "01".

It would have an intermediate state that is reached from the initial state on reading a "00" and has an ε-transition back to the initial state. Finally, there would be an accepting state that is transitioned to from the intermediate state on reading another "00".

Other requests in the question involve constructing NFAs with different numbers of states and for different languages, each of which has its own set of transitions and accepting conditions.

NFAs are used to recognize patterns in computer science and can exhibit complex behavior even with a small number of states.