QUESTION $1$

$[$Total marks: $10]$

$1(a)$

$[4$ Marks$]$

Given a binary alphabet $0,1,$ write a regular expression that recognises all words

that have an even number of $\text{'}1\text{'}$s and end with a $\text{'}0\text{'}.$

$1($b$)$

$[6$ Marks$]$

Use the subset construction method to derive a deterministic finite state automaton

that recognises the language from part $($a$).$

$[$End Question $1]$