Quantitative Formal Modeling and Worst-Case Performance Analysis from Coursera

Welcome to "Quantitative Formal Modeling and Worst-Case Performance Analysis," an intellectually stimulating course designed to hone your abstract thinking skills in the realm of theoretical computer science.

This course invites you to dive deep into the world of token production and consumption, a foundational approach to system behaviour. Master the art of mathematically formalizing these concepts through prefix orders and counting functions. Get hands-on with Petri-nets, explore the nuances of timing, and delve into the scheduling intricacies of token systems. You'll even learn to conduct worst-case performance analysis on single-rate dataflow graphs, examining key metrics like throughput, latency, and buffering.

Why the focus on small examples rather than industrial-size systems? The aim here is twofold: First, we strive to cultivate your ability to think abstractly and mathematically about modelling and performance—a vital skill for tackling any future challenges in this field. Second, while dataflow techniques are indeed industry-applicable, this course serves as an essential primer that focuses on single-rate dataflow, the cornerstone of more advanced dataflow techniques.

And here's a bonus: this course forms part of the esteemed Quantitative Evaluation of Embedded Systems (QEES) curriculum offered under the aegis of the EIT-Digital University and the Dutch 3TU consortium. While the examination for QEES is more advanced, this course perfectly mirrors its initial three-week content, offering you a robust academic experience online.

Ready to sharpen your abstract thinking and delve into the fascinating world of formal modelling? Enroll now to secure your spot.

What's inside

Syllabus

Introduction

This course is part of a Blended Master Programme in Embedded Systems.

Modeling systems as token consumption/production systems

In this module/week you will learn to draw a model of a token consumption/production system, and communicate your interpretation of this model with others in an informal manner. At the end of this model, you will be able to draw your own models, and explain your interpretation of them in general terms. Also, you will know about the standard Petri-net interpretation of consumption/production systems, and will be able to point out particular patterns in Petri-net models. Finally, you will be able to refine a consumption/production model into a model that contains sufficient information to allow worst-case performance analysis. This is all tested using a peer-reviewed assignment.

Syntax and semantics

In this module/week, you will be really training your abstract thinking skills. After finishing this module, you will have learned how to formalize the behavior of any dynamical system as a prefix order, and how to formalize the interpretation of a consumption/production system as a counting function on such a prefix order. You understand how the Petri-net interpretation puts certain restrictions on these counting functions, and how you can exploit those restrictions to prove properties about Petri-net interpretations, without knowing the actual interpretation itself. At the end of the module, you will practice the formalization of performance metrics as logical properties of counting functions, by recognizing right and wrong examples of formalization. Those who are already familiar with Petri-net theory, may find that the prefix order semantics that I introduce in this course is slightly different from what they are used to. Traditional Petri-net semantics is usually based on markings, transition systems, or the execution trees thereoff. Execution trees are a particular example of a prefix order, but in general prefix orders offer the added flexibility that they do not restrict the user to discrete interpretations of behavior only. This is particularly suitable when seeking connection between theoretical computer science and an application field like embedded systems, from which this course originates, where also the continuous behavior of physical systems has to be taken into account.

Performance analysis

In this module/week you will learn to exploit the structure of single-rate dataflow graphs to perform worst-case analysis of performance metrics like throughput, latency and buffering. After this week, you know how to calculate the maximum cycle mean of a dataflow graph, how to construct a periodic schedule for it, how to optimize this schedule for latency analysis, and how to determine the size of buffers with back-pressure such that the worst-case analysis remains valid. If you understood the material of the previous module/week, the proofs presented in this week will give you a deeper understanding of the mathematical underpinning of these methods.

One final example

In this last week, we just discuss one more example, following the outline of the peer-reviewed assignment of the first module/week. It's just a little summary, combining everything we have learned so far, and there is some additional reading material to trigger an appetite for further discovery.

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Develops abstract thinking skills in theoretical computer science, which is instrumental for addressing challenges in the field

Provides a solid primer on dataflow techniques, essential for industry application

Taught by Anne Remke and Dr.ir. Pieter Cuijpers, recognized experts in the field of embedded systems

Designed for students enrolled in the Blended Master Programme in Embedded Systems, indicating academic rigor and relevance

Reviews summary

Confusing but interesting course

According to students, this challenging yet interesting course is well received but it could be more improved by providing further explanations and clearer instructions. Many students have complained about the instructor's teaching style and communication skills, while others have praised their clarity and engaging style. Note that the sample size is small, so take these reviews with a grain of salt.

Instructor has a clear and engaging teaching style.

"Excellent course."

"Also the teacher has a very clear and engaging style."

Instructor needs to improve communication and explanations.

"No explanation."

"Worst course ever. Instructor needs to improve."

"All the time with his body before the pictures and nets."

Concepts could be explained more clearly.

"Could be more clear about how to calculate period and latency."

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Quantitative Formal Modeling and Worst-Case Performance Analysis with these activities:

Refresher: Discrete mathematics

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Prepare for the course by reviewing the basics of discrete mathematics.

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Review your notes or textbooks on discrete mathematics.
Focus on topics like set theory, logic, and counting principles.
Solve practice problems to test your understanding.
Consider taking an online quiz or assessment to gauge your readiness.
Reach out to the course instructor or classmates for assistance if needed.

Study Petri Nets: Theory and Practice

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Strengthen your understanding of Petri nets, a key concept in this course, by reading this in-depth book.

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Obtain a copy of the book.
Read through the chapters relevant to the course.
Take notes and highlight important concepts.
Complete the exercises and assignments found in the book.
Discuss the book's content with classmates or the course instructor.

Practice with token production and consumption

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Put the course materials into practice by solving drills that focus on token production and consumption.

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Set up your practice environment with the materials provided by the course instructor.
Review the concepts of token production and consumption.
Begin solving the practice drills.
Check your answers against the provided solutions.
Reach out to the course instructor or peers for help if needed.

Five other activities

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Form a study group with classmates

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Collaborate with peers to reinforce your understanding of course concepts and improve your learning experience.

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Identify a group of classmates who are interested in forming a study group.
Establish regular meeting times and decide on a meeting format (e.g., in-person, online).
Discuss course materials, work on assignments together, and quiz each other.
Share resources and provide support to each other.
Reflect on your progress and make adjustments as needed.

Design a Petri net model for a simple system

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Apply the course concepts by designing and creating a Petri net model of a simple system.

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Identify a simple system to model (e.g., a vending machine, traffic light).
Research Petri nets and their components.
Design the Petri net model for the chosen system.
Validate the model by simulating it and checking its behavior.
Document your model and findings.

Practice applying worst-case performance analysis

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Enhance your understanding of worst-case performance analysis by practicing on a variety of problems.

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Review the concepts of worst-case performance analysis.
Solve practice problems involving throughput, latency, and buffering.
Check your answers against the provided solutions.
Discuss your solutions with classmates or the course instructor.
Identify areas where you need further practice.

Develop a visual guide to prefix order semantics

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Deepen your understanding of prefix order semantics by creating a visual representation that explains its concepts.

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Gather materials and resources on prefix order semantics.
Design and outline the visual guide.
Create the visual guide using appropriate software or tools.
Validate your guide by sharing it with peers or the course instructor for feedback.
Revise and finalize the visual guide based on feedback.

Contribute to a Petri net simulation tool

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Enhance your practical skills and contribute to the community by participating in an open-source Petri net simulation tool project.

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Identify an open-source Petri net simulation tool project to contribute to.
Review the project's documentation and codebase.
Identify an area where you can make a meaningful contribution.
Develop a feature, fix a bug, or improve the documentation.
Submit a pull request with your changes.

Career center

Learners who complete Quantitative Formal Modeling and Worst-Case Performance Analysis will develop knowledge and skills that may be useful to these careers:

Management Consultant

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Financial Analyst

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Economist

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Data Engineer

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Machine Learning Engineer

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Operations Research Analyst

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Quantitative Analyst

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Software Engineer

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Systems Analyst

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