Let L be the language in which the third symbol from the right is a. Give a non-deterministic finite automaton that recognizes L.
Third input symbol is a while reading the input symbol from RHS
$(a's\ or\ b's)\ a\fbox{aa}$
$(a's\ or\ b's)\ a\fbox{ab}$
$(a's\ or\ b's)\ a\fbox{ba}$
$(a's\ or\ b's)\ a\fbox{bb}$
Firstly try to draw 4 states namely $aaa,aab,aba,abb$ from the initial state and name the intermediate states along with it.
Now in-order to find out what are the transitions for $aaa,aab,aba,abb$ you can do the following:
$aaa \overset{b}{\rightarrow} a\fbox{aab}$
$aaa \overset{a}{\rightarrow} a\fbox{aaa}$
$aba \overset{b}{\rightarrow} a\fbox{bab}$
$aba \overset{a}{\rightarrow} a\fbox{baa}$
.
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$ \&\ likewise$