Question: Answer all parts for the following DFA and give reasons for your answers.

$$\begin{gathered} \mathbf{\text{a.Is}}<M,0100>\mathbf{\in }{\mathit{A}}_{\mathbf{D}\mathbf{F}\mathbf{A}}\mathbf{}\mathbf{}\mathbf{?}\mathbf{} \\ \mathit{b}\mathbf{.}\mathbf{}\mathit{I}\mathit{s}\mathbf{}\mathbf{}<M,011>\mathbf{\in }{\mathit{A}}_{\mathbf{D}\mathbf{F}\mathbf{A}}\mathbf{?}\mathbf{} \\ \mathit{c}\mathbf{.}\mathbf{}\mathit{I}\mathit{s}\mathbf{}<M>\mathbf{\in }{\mathit{A}}_{\mathbf{D}\mathbf{F}\mathbf{A}}\mathbf{}\mathbf{?}\mathbf{} \\ \mathit{d}\mathbf{.}\mathbf{}\mathit{I}\mathit{s}\mathbf{}<M,0100>\mathbf{\in }{\mathit{A}}_{\mathbf{R}\mathbf{E}\mathbf{X}}\mathbf{}\mathbf{?}\mathbf{} \\ \mathit{e}\mathbf{.}\mathbf{}\mathit{I}\mathit{s}<M>\mathbf{\in }{\mathit{E}}_{\mathbf{D}\mathbf{F}\mathbf{A}}\mathbf{}\mathbf{}\mathbf{?}\mathbf{} \\ \mathit{f}\mathbf{.}\mathbf{}\mathit{I}\mathit{s}\mathbf{}<M,M>\mathbf{\in }\mathit{E}{\mathit{Q}}_{\mathbf{D}\mathbf{F}\mathbf{A}}\mathbf{}\mathbf{}\mathbf{?} \end{gathered}$$

A Deterministic Finite Automata is the computational model that determines the state of the input symbol provided.

a.

Consider the given diagram, assume that the states are named as follows,

, represents the inputs of the machine. Symbol 0 starts with the state S , the next input 1 takes to the state A . The input symbol 0 moves to the state B and the next input 0 is the last symbol of the string that ends in the state S ,which accepts the input.

Therefore, Yes, .

b.

Consider the given diagram, assume that the states are named as follows,

, represents the inputs of the machine. Symbol 0 starts with the state S , the next input 1 takes to the state A . The input symbol 0 is the last symbol of the string that ends in the state B ,which doesnot accepts the input.

Therefore, No, .

c.

Consider the given diagram, assume that the states are named as follows,

, represents the inputs of the machine. The input symbol empty is not accepted by the given automata.

Therefore, No,role="math" .

d.

Consider the given diagram, assume that the states are named as follows,

, represents the inputs of the machine. The input symbol is belongs to DFA not the regular language inputs.

Therefore, No,

e.

Consider the given diagram, assume that the states are named as follows,

, represents the empty input of the machine. The input symbol is belongs to DFA not the regular language inputs.

Therefore, No,.

e.

Consider the given diagram, assume that the states are named as follows,

, represents the same language of the machine. The input symbol belongs to the DFA.

Therefore, Yes,.