Problem $3.$ Asynchronous Processes $[25$ points$]$ In this problem, we are

going to model a distributed processing system. This system has two kinds of

processes: a manager and a worker process. In our system we will assume

that there is a single manager process and $10$ worker processes. Remember that

asynchronous processes are a collection of tasks, each task has a guard, only

when the task$-$guard is true can the task$-$update execute. Each process can

maintain any number of state variables.

The manager process is as follows:

Initially, it sends true on the activate output to each worker processes.

It receives status signals from each worker when the worker status changes.

It maintains a count of the number of workers whose status is true. Initially

this count is $($obviously$)$ zero. $($The details on how worker status toggles will be

described in the worker process$).$

It has a task to process a load input from any worker. The value of this

input is two numbers: the first indicating the load value and the second is the

ID of the worker process.

If the load value of the sending worker is higher than the integer LIMIT,

then it enables the stopWorker $($i$)$ task. In this task, the manager sends false

on the activate output to the $i^{th}$ worker. If it is lower than LIMIT, no action

is taken.

The manager process has a permanently enabled task that randomly chooses

any worker process to which it has previously sent a "deactivation" signal and

sends it a true on the corresponding activate output.

Each worker process is as follows:

Each worker process maintains a counter called load that is initialized to $0.$

Initially, the worker process is OFF. When it receives a true on its activate

input, it turns ON$.($You can model the process turning on or off with a perma$-$

nently enabled task$).$

If the worker process is ON $,$ it has four kinds of tasks that are enabled. The

take Job task increases the counter by a random integer in $1,3.$ The doneJob

task decreases the counter by $1$ if it is greater than $0.$ Otherwise, it has no

effect. The reportStatus task sends the value true on its attatus output. The

sendLoad task sends the value of the counter $($load$)$ and the ID of the worker

process to the manager process.

If the worker process is OFF, the reportStatus task is enabled and sends

the value false on its status output. Tasks takeJob, doneJob, and sendLoad

are disabled.

If the worker process is ON and it receives false on its activate input, then

it turns OFF. In the OFF state, the coolOff task is enabled. In this task, if

the load value is non$-$zero, it decreases the load value by $1.$

If the worker process is OFF and it receives a true on its activate input but

the load value is not zero, the activation is remembered, but the process does

not become ON till the load value becomes zero. if the load value is zero when

true is received on the activate signal, then the worker process turns ON$.$

Describe each process using either the asynchronous reactive component

formalism or as an extended state machine. Please show only one representative

worker process! Do not draw $10$ of them. Clearly identify the inputs, outputs,

and states of each process and describe their types. Comment on whether each

process is finite or infinite state, and deterministic or nondeterministic.