Create a DFA called M$1$ that recognizes the language of strings of a$\text{'}$s and b$\text{'}$s having a length of exactly $2.$

Show a logical analysis of the states in M$1.$

Create a DFA called M$2$ that recognizes the language of a$\text{'}$s and b$\text{'}`$s that contains zero or more as followed by one or more bs$.$

Show a logical analysis of the states in M$2.$

Use the algorithm from class to write Grafstate code for a DFA called M that recognizes the language L$($M$1)$L$($M$2).$

Show a logical analysis of the states in M$.$

Identify which states in M are not necessary.

A state is not necessary if the state does not contribute to the computation of any string$$

Considering the logical purpose of the states used M$1$ and M$2,$ explain why the states identified in problem are not necessary and why the Union algorithm produced them.

Modify your Grafstate code from problem to produce an equivalent DFA that does not have any states that are not necessary.

Two DFAs M$1$ and M$2$ are said yo be equivalent $($written M$1\backslash$cong M$2)$ if L$($M$1)=$L$($M$2).$Create a DFA called M$1$ that recognizes the language of strings of a$\text{'}$s and b$\text{'}$s having a length of exactly $2.$

Show a logical analysis of the states in M$1.$

Create a DFA called M$2$ that recognizes the language of a$\text{'}$s and b$\text{'}`$s that contains zero or more as followed by one or more bs$.$

Show a logical analysis of the states in M$2.$

Use the algorithm from class to write Grafstate code for a DFA called M that recognizes the language L$($M$1)$L$($M$2).$

Show a logical analysis of the states in M$.$

Identify which states in M are not necessary.

A state is not necessary if the state does not contribute to the computation of any string$$

Considering the logical purpose of the states used M$1$ and M$2,$ explain why the states identified in problem are not necessary and why the Union algorithm produced them.

Modify your Grafstate code from problem to produce an equivalent DFA that does not have any states that are not necessary.

Two DFAs M$1$ and M$2$ are said yo be equivalent $($written M$1\backslash$cong M$2)$ if L$($M$1)=$L$($M$2).$