written 7.0 years ago by | • modified 2.9 years ago |
Convert the following NFA to a reduced DFA(final state is marked by *)
$\delta$ | 0 | 1 |
---|---|---|
p | p,q | r |
q | r | r |
r | s | --- |
$^*s$ | s | s |
written 7.0 years ago by | • modified 2.9 years ago |
$\delta$ | 0 | 1 |
---|---|---|
p | p,q | r |
q | r | r |
r | s | --- |
$^*s$ | s | s |
written 7.0 years ago by |
The NFA that is made from the table is as follows:
Now, as {p} is initial state, it is added to the solution
We take the state transitions of all states for each input
$\delta({p},0)={p,q}$
Therefore, {p,q} is added to the solution
$\delta({p},1)={q}$
$\delta({q},0)={r}$
Therefore, {r} is added to the solution
$\delta({q},1)={r}$
$\delta({r},0)={s}$
Therefore, {s} is added to the solution
$\delta({r},1)=\Phi$
$\delta({s},0)={s}$
$\delta({s},1)={s}$
$\delta({p,q},0)={p,q,r}$
Therefore, {p,q,r} is added to the solution
$\delta({p,q},1)={q,r}$
Therefore, {q,r} is added to the solution
$\delta({p,q,r},0)={p,q,r,s}$
$\delta({p,q,r},1)={q,r}$
$\delta({q,r},0)={r,s}$
Therefore, {r,s} is added to the solution
$\delta({q,r},1)={r}$
$\delta({r,s},0)={s}$
$\delta({r,s},1)={s}$
Therefore, the solutions set S ={{p,q},{r},{s},{p,q,r},{q,r},{r,s},{q,r,s}}