uestion 1: For each of the following problems: (a) Specify the language using text, $e, 8 . L=\{\ldots\}$ (b) Draw the DFSM that accepts the language. (c) Write the configurations for the computations of the given input strings and indicate if the machine accepts of rejects the string. Problems: 1. Strings over $\{a, b\}^{*}$ that contains no more than one $b$. Input strings: aa, aba, aabba, ababb, abababaaa. 2. Strings over $\{a, b\}^{*}$ where every $a$ is followed by $a b$. Input strings: bbb, abbb, baabb, abababa, bababab. 3. Strings over $\{a, b\}^{*}$ that begins and ends with an a or begins and ends with a b. Input strings: aa, aba, aabba, bbabab, abab, babaaa. 4. Strings over $\{a, b\}^{*}$ where two consecutive a's are followed by a b. Input strings: aa, aba, bba, aabba, aabbaa, aabba, ababb, bbaaabaab. Question 2: A DFSM $M_{1}$ is formally describes as $\{91, 92, 9 3, 94, 95},\{x, y\}, 93, \{q 3\}, delta$ ) where delta is given by the transition table below. Draw the DFSM that corresponds with $M_{1}$. \begin{tabular}{[1]111]} \hline & $X$ & $y$ \hline$q 1$ & $q 1$ & $q 2$ \hline$q 2$ & $q 1$ & $9 3$ \hline$q 3$ & $q 2$ & $q 4$ \hline$q 4$ & $q 3$ & $q 5$ \ \hline$q 5$ & $q 4$ & $q 5$ \ \hline \end{tabular) SE.SD.016