Question: (1) Create a DFA called M_1 that recognizes the @lang of strings of *{a}s and *{b}s having a length of 2. // Show a logical

(1) Create a DFA called M_1 that recognizes the @lang of strings of *{a}s and *{b}s having a length of 2. // Show a logical analysis of the states in M_1. //

(2) Create a DFA called M_2 that recognizes the language of *{a}s and {b}s that contain 2 consecutive *{a}s. // Show a logical analysis of the states in M_2. //

(3) Use the !{algorithm from class} to write \graf code for a DFA called M that recognizes the @lang L(M_1)\uL(M_2). // Show a logical analysis of the states in M. //

(4) Identify which states in M are not necessary. [i] A state is *{not necessary} if the state does not contribute to the computation of *{any} string/ //

(5) Considering the logical purpose of the states used M_1 and M_2, explain why the states identified in problem @{(7)} are not necessary and why the Union algorithm produced them. //

(6) Modify your \graf code from problem @{(3)} 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~=M_2) if L(M_1)=L(M_2).

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