Figure $1$: $2$ automata A and B

Let us consider the system $G2$ given Figure $2$ where the set of observable events is given by $E_o=$

$\{a,b,c\},$ the set of regular unobservable events is $E_{\text{u}\text{o}\text{r}}=\{{}_1\}$ and the set of faulty events is given

by $E_F=\{{}_f\}.$

$($a$)$ Give a list of $10$ observable words with their associated set of consistent paths and the associ$-$

ated diagnosis results.

$($b$)$ Give the diagnoser of the system $G2.$

$($c$)$ Give the list of uncertain cycles and the list of certain cycles.

$($d$)$ Give the list of undeterminate cycles.

$($e$)$ Conclude on the diagnosability of the systems $G2.$

Let us consider the system $G3$ given Figure $3$ where the set of observable events is given by $E_o=$

$\{a,b\},$ and the set of faulty events is given by $E_F=\{{}_f\}.$

$($a$)$ Give the diagnoser of the system $G3.$

$($b$)$ Give the list of uncertain cycles and the list of certain cycles.

$($c$)$ Give the list of undeterminate cycles.

$($d$)$ Conclude on the diagnosability of the systems G$3.$ Figure $3$: G$3$

Let us consider the system $G4$ given Figure $4$ where the set of observable events is given by $E_o=$

$\{a,b\},$ and the set of faulty events is given by $E_F=\{{}_f\}.$

$($a$)$ Give the diagnoser of the system $G4.$

$($b$)$ Build the twin machine.

$($c$)$ Give an example of a critical pair.

$($d$)$ Conclude on the diagnosability of $G4$

Figure $4$: G$4$