Requirement Specifications for Autonomous Systems from Coursera

This course will discuss different ways of formally modeling requirements of interest for autonomous systems. Examples of such requirements include stability, invariance, reachability, regular languages, omega-regular languages, and linear temporal logic properties. In addition, it will introduce non-deterministic finite and büchi automata for recognizing, respectively, regular languages and omega-regular languages.

This course can be taken for academic credit as part of CU Boulder’s MS in Computer Science degrees offered on the Coursera platform. These fully accredited graduate degrees offer targeted courses, short 8-week sessions, and pay-as-you-go tuition. Admission is based on performance in three preliminary courses, not academic history. CU degrees on Coursera are ideal for recent graduates or working professionals. Learn more:

MS in Computer Science: https://coursera.org/degrees/ms-computer-science-boulder

What's inside

Syllabus

Course Introduction

In this course, we delve into both low-level and high-level specifications, fundamental to the development of safe autonomous systems. This module is specifically designed to equip students with an in-depth understanding of expressing system behaviors through formal methods, including linear temporal logic and automata on both finite and infinite strings. Through a collection of detailed examples and practical applications, participants will acquire the skills needed to define and analyze key properties of autonomous systems, such as safety and reachability.

Low-Level Specifications

This module offers a concise introduction to normed vector spaces and stability concepts in autonomous systems, encompassing both asymptotic stability and global asymptotic stability. It emphasizes the application of Lyapunov's Stability Theorem for the formal verification of these properties in complex systems, including its application to various simple systems, such as linear ones. Through illustrative examples, we will demonstrate the significance of these concepts in analyzing and ensuring the stability of systems.

High-Level Specifications: Reachability, Safety, Regular and ω-Regular Properties

Delve into the topic of reachable sets and uncover their critical role in guaranteeing system safety. This module introduces frameworks for exploring computational techniques to over-approximate reachable sets across diverse system classes. You will have the chance to apply your knowledge in real-world contexts, investigate the use of zonotopes, and recognize their beneficial properties in the computation of reachable sets. Moreover, we delve into fundamental concepts of formal languages, and regular and omega-regular expressions, offering succinct and formal methods to express regular and omega-regular languages, respectively.

Nondeterministic Finite and Büchi Automata (NFA and NBA)

This module immerses you in the essential principles of regular and ω-regular properties and how they are represented via non-deterministic finite automata (NFA) and Büchi automata (NBA), respectively. You will study the notation and architecture of NFAs and NBAs, master the construction of regular and ω-regular expressions, and grasp their correlation with these automata. The course will navigate you through the conversion of NFAs to regular expressions and NBAs to ω-regular expressions and the inverse, elucidating the significance of these concepts in the verification of finite and infinite behaviors of systems.

Linear Temporal Logic Formulae

This module provides an in-depth exploration of Linear Temporal Logic (LTL) formulas, a mathematical formalism for describing languages containing infinite words. It presents a framework for articulating the temporal dimensions of system behaviors, offering a syntax that closely mirrors natural language. By melding propositional logic with temporal operators, LTL furnishes a powerful toolkit for specifying the rich behaviors of systems.

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

This course provides a comprehensive introduction to formal methods for modeling requirements of autonomous systems and their behaviors

Suitable for intermediate learners seeking to strengthen their foundation in formal methods

Potential dealbreaker: Requires learners to have basic knowledge in systems engineering or similar

Covers key concepts in non-deterministic finite and büchi automata

Examines formal languages, regular and omega-regular expressions, offering a structured approach to specifying system behaviors

Leverages linear temporal logic formulae to describe the temporal dimensions of system behaviors

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 Requirement Specifications for Autonomous Systems with these activities:

Review Linear Algebra

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Ensure a solid foundation by reviewing the principles of linear algebra.

Browse courses on Linear Algebra

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Review the basics of vector spaces.
Practice matrix operations.
Solve systems of linear equations.

Glossary of Key Terms

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Build a strong foundation by creating a comprehensive glossary of key terms used in the course.

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Review the course materials.
Identify and define the key terms.
Organize the terms in a logical manner.

Tutorials on Nondeterministic Automata

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Supplement your understanding through tutorials on nondeterministic automata, a core concept in this course.

Browse courses on Regular Expressions

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Find tutorials on nondeterministic automata.
Watch or read the tutorials.
Complete the exercises or quizzes provided in the tutorials.

Eight other activities

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Review: Introduction to Automata Theory, Languages, and Computation

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Enhance your understanding by reading a foundational text in the field of automata theory, languages, and computation.

View Introduction to Automata Theory, Languages, And... on Amazon

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Read the assigned chapters.
Complete the exercises at the end of each chapter.
Summarize the key concepts.

Practice Questions on Reachability

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Strengthen your understanding of reachability by solving practice problems.

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Review the concept of reachability.
Solve practice problems on reachability.
Check your answers.

Practice reachability analysis

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This activity will provide you with hands-on experience in applying the techniques of reachability analysis, a key concept in autonomous systems.

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Choose a simple autonomous system, such as a unicycle robot.
Define the state space of the system.
Develop a reachability analysis algorithm.
Implement the algorithm in a programming language of your choice.
Apply the algorithm to the autonomous system to compute its reachable states.

Develop a Requirements Specification using LTL

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Gain practice applying LTL to a real-world problem by creating a requirements specification for an autonomous system.

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Identify the system and its requirements.
Model the system using LTL.
Write the requirements specification using LTL.
Validate the requirements specification.

Develop a Visual Representation of Automata

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Enhance your comprehension by creating visual representations of automata, making these complex concepts more intuitive.

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Choose an automaton to represent.
Design a visual representation.
Create the visual representation.

Design a Büchi automaton to represent a safety requirement

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Designing a Büchi automaton for a safety requirement will help you master the techniques of formal specification and verification of autonomous systems.

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Identify a safety requirement for an autonomous system.
Translate the requirement into a Büchi automaton.
Draw the state diagram of the automaton.
Write a formal specification of the automaton.
Verify that the automaton satisfies the safety requirement.

Design a Stability Analysis Prototype

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Apply the concepts of stability analysis to a specific system by designing a prototype.

Browse courses on Stability

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Choose a system to analyze.
Develop a mathematical model of the system.
Apply Lyapunov's Stability Theorem to the system.
Design a prototype to demonstrate the stability analysis.

Develop a prototype of an autonomous navigation system

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This project will allow you to apply the concepts learned in the course to a real-world problem and gain practical experience in autonomous systems development.

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Define the requirements for the navigation system.
Design the architecture of the system.
Implement the system in a programming language of your choice.
Test and evaluate the system.
Deploy the system on a real-world platform.

Career center

Learners who complete Requirement Specifications for Autonomous Systems will develop knowledge and skills that may be useful to these careers:

Safety Engineer

Safety Engineers apply engineering principles to design and implement systems that are safe for human use. They use their knowledge of engineering and safety to identify and mitigate potential hazards. This course can help Safety Engineers build a foundation in formal methods for specifying and analyzing system requirements, which is essential for ensuring the safety of autonomous systems.

See salaries and explore the career path for Safety Engineer

Systems Analyst

Systems Analysts study the needs of organizations and develop solutions to meet those needs. They often work with engineers and other technical staff to design and implement new systems or improve existing ones. This course can help Systems Analysts build a foundation in formal methods for specifying and analyzing system requirements, which is essential for ensuring the safety and reliability of complex systems.

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Software Engineer

Software Engineers design, develop, and test software systems. They use their knowledge of computer science and engineering to create software that meets the needs of users. This course can help Software Engineers build a foundation in formal methods for specifying and analyzing system requirements, which is essential for ensuring the safety and reliability of software systems.

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Project Manager

Project Managers plan, organize, and execute projects. They work with stakeholders to define project goals, develop project plans, and track project progress. This course can help Project Managers build a foundation in formal methods for specifying and analyzing system requirements, which is essential for ensuring the success of complex projects.

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Business Analyst

Business Analysts study the needs of organizations and develop solutions to meet those needs. They often work with stakeholders to define business requirements and develop business plans. This course can help Business Analysts build a foundation in formal methods for specifying and analyzing system requirements, which is essential for ensuring the success of business projects.

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Quality Assurance Analyst

Quality Assurance Analysts test software systems to ensure that they meet the needs of users. They use their knowledge of software testing to identify and fix bugs. This course can help Quality Assurance Analysts build a foundation in formal methods for specifying and analyzing system requirements, which is essential for ensuring the quality of software systems.

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Data Scientist

Data Scientists use their knowledge of data science to extract insights from data. They use their skills in statistics, machine learning, and data visualization to develop models and algorithms that can help organizations make better decisions. This course can help Data Scientists build a foundation in formal methods for specifying and analyzing system requirements, which is essential for ensuring the accuracy and reliability of data-driven models.

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Machine Learning Engineer

Machine Learning Engineers design, develop, and deploy machine learning models. They use their knowledge of machine learning and engineering to create models that can learn from data and make predictions. This course can help Machine Learning Engineers build a foundation in formal methods for specifying and analyzing system requirements, which is essential for ensuring the safety and reliability of machine learning models.

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Artificial Intelligence Engineer

Artificial Intelligence Engineers design, develop, and deploy artificial intelligence systems. They use their knowledge of artificial intelligence and engineering to create systems that can learn from data, make decisions, and solve problems. This course can help Artificial Intelligence Engineers build a foundation in formal methods for specifying and analyzing system requirements, which is essential for ensuring the safety and reliability of artificial intelligence systems.

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Computer Scientist

Computer Scientists conduct research in the field of computer science. They use their knowledge of computer science to develop new algorithms, data structures, and programming languages. This course can help Computer Scientists build a foundation in formal methods for specifying and analyzing system requirements, which is essential for ensuring the correctness and efficiency of computer programs.

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Electrical Engineer

Electrical Engineers design, develop, and test electrical systems. They use their knowledge of electricity and engineering to create systems that meet the needs of users. This course may be helpful for Electrical Engineers who want to learn more about formal methods for specifying and analyzing system requirements.

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Mechanical Engineer

Mechanical Engineers design, develop, and test mechanical systems. They use their knowledge of mechanics and engineering to create systems that meet the needs of users. This course may be helpful for Mechanical Engineers who want to learn more about formal methods for specifying and analyzing system requirements.

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Civil Engineer

Civil Engineers design, develop, and test civil systems. They use their knowledge of civil engineering and engineering to create systems that meet the needs of users. This course may be helpful for Civil Engineers who want to learn more about formal methods for specifying and analyzing system requirements.

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Chemical Engineer

Chemical Engineers design, develop, and test chemical systems. They use their knowledge of chemistry and engineering to create systems that meet the needs of users. This course may be helpful for Chemical Engineers who want to learn more about formal methods for specifying and analyzing system requirements.

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Biomedical Engineer

Biomedical Engineers design, develop, and test biomedical systems. They use their knowledge of biomedical engineering and engineering to create systems that meet the needs of users. This course may be helpful for Biomedical Engineers who want to learn more about formal methods for specifying and analyzing system requirements.

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