This question is about Simple Temporal Networks $($STNs$)$ and Simple Temporal Networks with

Uncertainty $($STNUs$).$

$($a$)$ Consider the following statements:

$-$ I leave for work between $7$:$50$ and $8$:$00($t$0).$

$-$ I arrived at work before $9$:$00($t$4).$

$-$ It takes me $10$ to $15$ minutes to reach the station $($t$1).$

$-$ The train arrives at $8$:$20($t$2).$

$-$ The train journey takes between $30$ and $50$ minutes $($arriving in station at t$3).$

The following Simple Temporal Network $($STN$)$ graph illustrates the temporal constraints for the

problem. Note that:

$-$ In an STN all of the timepoints are controllable.

$-$ The value $$inf$$ indicates infinity, or $$no upper bound$.$

$($i$)$ Is the STN consistent? If so$,$ provide a valid assignment that satisfies the constraints.

$($ii$)$ Draw the STN in single bound format.

$($b$)$ Suppose that the train journey takes exactly $45$ minutes. Is the STN still consistent? If not, how

can this be checked in the $($single$-$bound$)$ STN graph?

$($c$)$ Suppose instead that the train journey takes $30$ to $50$ minutes, but that walking to the station $(10$

to $15$ minutes$)$ and the train journey $(30$ to $50$ minutes$)$ are uncontrollable durations. The problem can

now be represented as an STNU with contingent links for those durations.

$($i$)$ Is the STNU strongly controllable? If not, explain why not.

$($ii$)$ Is the STNU weakly controllable? If not, explain why not.