Consider the following assumption regarding the vacuum$-$cleaner agent we

discussed in class:

$$ The performance measure awards one point for each clean square at each time step

over a $$lifetime$$ of $1000$ time steps.

$$ The $$geography$$ of the environment is known apriori $($see vacuum cleaner slide

showing cells A and B$,$ etc.$)$ but the dirt distribution and the initial location of the

agent are not. Clean squares stay clean and sucking cleans the current square. The

Left and Right actions move the agent left and right except when this would take

the agent outside the environment, in which case hte agent remains where it is$.$

$$ The only available actions are Left, Right, and Suck. $($Note$,$ there is no NoOp$).$

$$ The agent correctly perceives its location and whether that location contains dirt.

a$.$ Prove that the simple vacuum$-$cleaner agent function described in class and given

the assumptions above is indeed rational.

b$.$ Describe a rational agent function for the case in whcih each movement costs one

point. Does the corresponding agent program require internal state?

c$.$ Discuss possible agent designs for the cases in which clean squares can become dirty

and the geography of the environment is unknown. Does it make sense for the agent

to learn from its experience in these cases? If so$,$ what should it learn? If not, why

not?