Quantitative Formal Modeling and Worst-Case Performance Analysis

EIT Digital via Coursera

Go to Course: https://www.coursera.org/learn/quantitative-formal-modeling-1

Introduction

**Course Review: Quantitative Formal Modeling and Worst-Case Performance Analysis** If you're venturing into the complex yet fascinating world of theoretical computer science, specifically within the realms of embedded systems, look no further than the *Quantitative Formal Modeling and Worst-Case Performance Analysis* course available on Coursera. This intellectually stimulating course bridges the gap between abstract theoretical concepts and practical applications, making it a valuable addition to any tech-savvy learner's repertoire. ### **Course Overview** This course delves into the intricacies of token production and consumption, a fundamental principle that defines system behavior. Participants will engage deeply with mathematical formalizations of these concepts using prefix orders and counting functions, gaining hands-on experience with Petri-nets, among others. The blended learning approach—part of a Master's program in Embedded Systems—allows for a mix of theoretical exploration and practical application. ### **Detailed Syllabus Breakdown** The course is divided into several thoughtfully crafted modules: 1. **Introduction to Token Consumption/Production Systems**: Participants will learn to model systems, translating complex behaviors into comprehensible diagrams. You will develop the ability to communicate your models clearly, refine them for performance analysis, and gain insights into standard Petri-net interpretations. This foundational knowledge paves the way for deeper exploration in later modules. 2. **Syntax and Semantics**: Prepare to sharpen your abstract thinking. This section focuses on formalizing the behavior of dynamical systems through prefix orders and counting functions. One of the standout features here is the course's unique take on Petri-net theory, distinguishing it from conventional methods by providing flexibility in interpretation. This module not only enhances your theoretical understanding but also emphasizes the connections to real-world applications, particularly in embedded systems. 3. **Performance Analysis**: This module is where the course truly shines in its practical application. Participants will learn to analyze worst-case performance metrics like throughput, latency, and buffering through dataflow graphs. By the end of this section, you will have the tools to calculate maximum cycle means, optimize schedules, and assess buffer sizes, linking theoretical insights directly to tangible performance outcomes. 4. **Final Example and Wrap-Up**: The course culminates in a comprehensive review of everything learned, reinforcing concepts while providing additional reading materials for further exploration. This wrap-up ensures a solid consolidation of knowledge and prepares students for more advanced inquiries into the field. ### **User Experience** The course employs a variety of teaching methods, including video lectures, peer-reviewed assignments, and interactive quizzes, which are key to reinforcing concepts. The peer-review component encourages collaboration and constructive feedback, enhancing the learning experience. Additionally, the course's structured pace accommodates students with varying levels of prior knowledge, making it accessible yet challenging. ### **Why You Should Enroll** 1. **Bridging Theory and Application**: This course is particularly beneficial for those looking to integrate theoretical knowledge with practical applications in embedded systems. 2. **Skill Development**: You'll not only learn modeling techniques but also sharpen your abstract thinking skills—crucial in theoretical computer science. 3. **Engaging Content**: The structured yet flexible approach ensures that irrespective of your background, you will find the course both engaging and intellectually rewarding. 4. **Career Advancement**: A solid understanding of quantitative modeling and performance analysis can significantly enhance your career prospects in fields related to system design, software engineering, and embedded systems. ### **Conclusion** *Quantitative Formal Modeling and Worst-Case Performance Analysis* is a profound course that melds theoretical knowledge with practical skill-building, appealing to both aspiring computer scientists and seasoned professionals seeking to refresh their knowledge. With its comprehensive syllabus and hands-on approach, this course prepares participants not only to understand but to apply intricate concepts of modeling and performance analysis in real-world systems. Whether you’re looking to upskill in your current role or transition into theoretical computer science, this course is highly recommended for anyone eager to explore the depths of system behavior and performance metrics. Do not miss the opportunity to elevate your understanding and applications in this field!

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.