What are the regular expressions to finite automata?

For each of the following languages, draw the finite automata (FA) accepting it.

{a,b}*{a}

The language states that the automata accept the strings containing any number of a's and b's and finally ending in a.

The finite state automaton for the language is as follows −

{a,b}*{b,aa}{a,b*}

The language states that the automata accept the strings starting and ending with any number of a's and b's and containing any of the substrings b and aa.

The finite state automaton for the language is a follows −

{bbb,baa}*{a}

The language states that the automata accept the strings containing any number of bbb's and baa's followed by a single a.

The final state automaton for the language is as follows −

{a}U{b}{a}*U{a}{b}*{a}

The language states that the automata accept the strings containing a,b followed by number of a's and stings starting with a followed by number of b's and end with a.

The finite state automaton for the language is as follows −