A malfunctioning garage door opener is defined by the transition graph below.

Unfortunately, $80\%$ of the time the system transitions from

'door opening' to 'door closing'. Write a Python simulation of

the system and simulate for a predefined number of time

steps to see if the system models the specification. If not,

output the counter$-$example. Base your code on the example

given in class. Include your code and an example output.

Consider including the following in your code:

# the atoms of the system

# the events

# the states of the system

# the state transition relation

# OPENING has $20\%$ chance of jumping directly to CLOSING by defn.

# the labeling function

#$----$ Define the event function.

def get$\_$event$($current$\_$state$)$:

#$----$ Define the decision function based on LTL formulas.

def hold$\_$properties$($current$\_$state, next$\_$state$)$:

#$----$ Perform probabilistic state transition, return next state

def transition$($current$\_$state$)$:

#$----$ Simulate state transitions

def simulate$($ initial$\_$state, num$\_$steps$)$: