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4. Constructing DFAs. For each of the following languages, give a DFA that decides it. You may give each DFA by defining its formal components, or as a state-transition diagram, whichever you prefer. Briefly justify your answers. (a) The language over alphabet \{a,b\} corresponding to $ab^$. (b) The language over alphabet \{a,b\} corresponding to $b(aaa)^b$.

          4. Constructing DFAs.
For each of the following languages, give a DFA that decides it. You may give each DFA by
defining its formal components, or as a state-transition diagram, whichever you prefer. Briefly
justify your answers.
(a) The language over alphabet \{a,b\} corresponding to $ab^*$.
(b) The language over alphabet \{a,b\} corresponding to $b(aaa)^*b$.

$4. Constructing DFAs. For each of the following languages, give a DFA that decides it. You may give each DFA by defining its formal components, or as a state-transition diagram, whichever you prefer. Briefly justify your answers. (a) The language over alphabet {a,b} corresponding to ab^*. (b) The language over alphabet {a,b} corresponding to b(aaa)^*b.$

Added by Sergio D.

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