Language Theory and Finite Automata

Assignment $-1$

$($Regular Languages$)$

Question $1$: Desing DFA for the given language descriptions $($preferred with minimum states$).[3$

marks$]$

A language the accepts words over alphabets $\{ab\}$ containing even number $a_s$ and odd

numbers of $b\text{'}$s or odd numbers of $a\text{'}$s and even numbers of $b\text{'}$s$.$

A language that accepts words over alphabets $\{a,b\}$ where number of $a_s{s}_{?}$ in a word must

be $3n+2$ with $n=0,1,2,$dots

For languages over $\{0,1\},$ strings representing binary numbers divisible by $7.$ Like $000,$

$111,1110$ etc.

Question $2$: Convert the given NFA to equivalent DFA by showing complete conversion process.

$[1$ mark$]$

Question $3$: Convert the NFA in Figure $1$ to equivalent Regular expression by showing complete

process. $[1$ mark$]$