For each of the languages below, draw the state diagram for a nondeterministic

finite automaton $($NFA$)$ to accept the language.

In order to get full marks,

your NFA must have at most the number of states specified

your NFA must take advantage of nondeterminism

There must be at least one case where the machine has a choice between two or more

next states on some input symbol, or at least one case where the machine has no possible

next state on a particular input symbol, or you must use $lon-$transitions $($in a non$-$trivial

way$).$

$($a$)L_1=\{\begin{array}{ccc}\text{w}\text{i}\text{n}& \{a,b,c,& d{\}}^{**}|\end{array}$ contains at least one sequence that consists of four or more of the

same character $\}$

Use no more than $21$ states.

$($Note: It can be done with $14$ states.$)$

$($b$)L_2=\{\begin{array}{ccc}\text{w}\text{i}\text{n}& \{a,b,& c{\}}^{**}|w=a^i{b}^j\end{array}$ where i and $j$ are both odd positive integers,

or $w=b^p{c}^q$ where $p$ and $q$ are positive integers and $q$ is a multiple of $3\}$

Use no more than $13$ states.