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## Problem 1

The trajectory planning subsystem of NASA’s Perseverance rover is highly critical and is comprised of 4
tasks. The first task performs motion course (MC) calculation every 10 ms, which takes at most 3.5 ms. The
second is in charge of performing sensor fusion (SF) between inertial measurements and incoming video feed.
SF operates at 100 Hz and its runtime varies anywhere between 3 and 7 ms.

for object detection (OD) and is activated at 25 Hz. OD can be carried out by analyzing the last batch of
video frames, which takes 8 ms in the worst case. Finally, a diagnostic (DG) task has a period of 24 ms and
a WCET of 12 ms.
a) Compute the minimum number of CPUs (if you had the perfect scheduler) necessary to consolidate all
the workload necessary to perform trajectory planning.
b) Consider the tasks in the order in which they appear in this question. Is is possible to schedule the
system via EDF-FF on a 2-CPU system?
c) Is it possible to use partitioned EDF to schedule the considered taskset on 2 CPUs?
d) Consider only the MG and DG tasks. Would it be possible to schedule them on the same CPU using
RM?
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CS-350 – Fundamentals of Computing Systems::Homework Assignment #7 Problem 2

## Problem 2

A sensor node needs to acquire and pre-process the data from 4 different onboard sensors. It is crucial that
pre-processing completes always before a new data sample is available at a given sensors to prevent loss of
samples. The sensors are the Gyroscope (G), Magnetometer (M), Accelerometer (A), and Baroscope (B).
The gyroscope produces data at a rate of 200 Hz, with each data sample requiring 2 ms for pre-processing in
the worst case.

Pre-processing for the magnetometer takes no longer than 1 ms with samples being produced
at 125 Hz. A new accelerometer sample is produced every 19 ms and pre-processing takes at most 4 ms.
Finally, pre-processing a barometer sample takes at most 6 ms, but the sampling period is configurable.

a) Without drawing the schedule, perform a back-of-the-envelope calculation to determine a suitable configuration for the sampling period of the barometer such that the system always operates correctly
under RM. For this part, consider only values of periods that are integers when expressed in milliseconds.
b) Because the calculation above returned a value of sampling period which is too large, you decide to set
the barometer sampling period to 29. Will the system operate correctly under RM?

c) You decide to set the barometer sampling period to 30 ms and stick to RM. You notice however that
once in a while (very rarely) the pre-processing of the accelerometer takes 5 ms instead of its nominal
4 ms worst-case execution time. When this happens, the system can still operate correctly if the
faulty accelerator pre-processing job is killed when it misses the deadline.

Killing any other
job is not acceptable. Also, you can apply a utilization-preserving transformation to all or some of
your tasks. Specifically, you can release any pre-processing task twice as fast but only perform half of
the required processing in each release. Explain how you can make the system operate correctly under
RM.

d) Consider the same system as the question above—i.e., where the period of the barometer has been set
to 30 ms. Compute the worst-case response (WCRT) time for all the jobs of each task.

e) Consider the same system as the question above—i.e., where the period of the barometer has been set
to 30 ms. How much slower can the processor be while still ensuring that all the deadlines are met?

f) Consider the same system as the question above—i.e., where the period of the barometer has been set
to 30 ms and the CPU has not been slowed down. Is the system schedulable under SJN?
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CS-350 – Fundamentals of Computing Systems::Homework Assignment #7 Problem 3

## Problem 3

Two processes, namely the Printer and the Shifter, co-operate to respectively print and update the value of
an array of integers that has a fixed size of 5 elements. The code executed by the Printer process is provided
in Listing 1; the code of the Shifter process is given in Listing 2.

If a variable has the same name in both
processes, it is to be considered a shared variable. A [FRAGMENT x] statement in the code refers to additional
lines of code (a fragment) to be inserted in place of the statement. At the beginning of time, both processes
start executing at their start line and will not run again once they reach their end line.

The initial state of
the shared data structures is as follows: array = [4, 9, 5, 3, 6]; queue = [8, 1, 7, 2] (NOTE: 8 is
at the head of the queue.)
1 Process Printer :
2 start {
3 tot = 0;
4
5 [ FRAGMENT P1 ]
6
7 for (i = 0; i < 5; ++ i) {
8 tot += array [i ];
9 } loop ;
10
11 [ FRAGMENT P2 ]
12

13 print ( tot );
14 } end ;
Listing 1: Code of Printer Process
1 Process Shifter :
2 start {
3 while (! queue . empty () ) {
4 prev = queue . pop () ;
5
6 [ FRAGMENT S1 ]
7

8 for (j = 0; j < 5; ++ j) {
9 tmp = array [ j ];
10 array [j] = prev ;
11 prev = tmp ;
12 } loop ;
13

14 [ FRAGMENT S2 ]
15
16 } loop ;
17 } end ;
Listing 2: Code of Shifter Process

a) Assume that P2 and S2 are empty and that (a) fragment P1 expands to wait(go); and (b) S1 expands
to if(queue.empty()){signal(go);}. Here, go is a semaphore initialized to 0. What is the maximum
value that could ever be printed at line 13 by the Printer process?

b) Assume that (a) fragment P1 and S1 expand to wait(m); and that (b) P2 and S2 expand to signal(m);.
Here, m is a semaphore initialized to 1. What is the maximum value that could ever be printed at line
13 by the Printer process?

c) Assume that fragments P1, P2, S1, and S2 are all empty. What is the maximum value that could ever
be printed at line 13 by the Printer process?
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CS-350 – Fundamentals of Computing Systems::Homework Assignment #7 Proble

## Problem 4

Code: In this problem you will write a function to navigate a complex multi-level structure that has an
emerging structure that is progressively revealed as the different hashes are cracked.

a) The code you have written in the previous assignments should have provided you with a basic unit,
namely the Dispatcher, capable of creating a work queue and distributing the work to a set of worker

In this problem, we will further extend the code to introduce a super-entity responsible for
coordinating the macro-phases of the processing flow. Because in the end the goal is to find a treasure,
we call the coordinating super-entity the Pirate.

Let us first review the processing problem at hand and then define the operating scope of the Pirate
entity. The file provided in input is still a list of hashes. Just like in the previous homework assignment,
the list contains hashes that can be immediately cracked and result in some non-negative integer
number.

Other hashes are impossible to crack. And other yet are crackable with a compound hint.
The idea is that the compound hint can be constructed from the integer values of the hashes that were
immediately crackable.

Specifically, as you crack those hashes that have a simple answer, your code will produce a sequence
of integers. Consider the sorted list of integers L = {A, B, C, D, . . .} such that A > B > C > D . . ..

Then, a compound hint has the form: “α; k; β” (this is literally a string formed by concatenating the
three numbers α, k, and β with the delimited character “;” in between!) where α and β are some
integers in L and such that α < β. Note that α and β are not necessarily contiguous in L. Finally, k
is any integer between α and β but different from them.

Moreover, no two compound hints share the
same α or β. So if a compound hint was of the form “α; k; β” (for some k), then there cannot exist
any compound hint with the form “α; k
0
; β” or “β; k
0
; γ” or “α; k
0

; γ” or “γ; k
0
; α” or “γ; k
0
; β”.

Let’s make an example. Suppose we have the following input file content:
202cb962ac59075b964b07152d234b70
d81f9c1be2e08964bf9f24b15f0e4900
03f206ba972ab43c585255d26826c4b3
37cba5957ccb647a5fb310923ac8794a

You will notice that the first and second hash can be reversed as “123” and “345”, respectively. While
the third and fourth hash appear to be initially uncrackable. We can then construct any compound
hint that follows the format “123; k; 345” and where k ∈ {124, . . . , 344}.

We then discover that the
fourth hash can be cracked with the compound hint “123;234;345”. The output produced by the code
should then be1
:
123
345
123;234;345
03f206ba972ab43c585255d26826c4b3

Write a Java class Pirate.java that defines a method called findTresure(…) that internally uses
the dispatcher to initially split the hashes in input to the worker threads. There are no restrictions
on the exact arguments and return value of this method, so use whatever you deem more appropriate.

The job of findTresure(…) is to coordinate the processing steps. After organizing the first run, it
collects the result from the worker threads (cracked hashes and timed out hashes) and organizes a new
run. In the second run, it will consider each pair of numbers α, β in the resulting L list and use the
1The order of the lines in the output is not important.
Problem 4 continued on next page. . . 5

CS-350 – Fundamentals of Computing Systems::Homework Assignment #7 Problem 4 (continued)
worker threads to check if any timed-out hashes can be cracked with a compound hint constructed
using α and β.

Apart from implementing the findTreasure(…) method, the class should also include a public
static void main(String [] args) function. The main(…) function should accept 3 parameters
from the calling environment. The path to the file is passed as the first parameter by the calling
environment.

The format of this file is the same as in the previous assignments. The second parameter
passed to your code is the number of available CPUs. The third parameter encodes the length of the
timeout for (currently) uncrackable hashes expressed in milliseconds.

It is responsibility of the main(…) function to internally invoke the implemented findTreasure(…)
method only once and make sure that the desired result is printed in output.
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CS-350 – Fundamentals of Computing Systems::Homework Assignment #7 Problem 5

## Submission Instructions:

in order to submit this homework, please follow the instructions below for
exercises and code.
The solutions for Problem 1-3 should be provided in PDF format, placed inside a single PDF file named

Follow the instructions on the class syllabus if you have not received
an invitation to join the Gradescope page for this class. You can perform a partial submission before the