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System Validation: Automata and behavioural equivalences

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Course Summary

Learn about the theory and practice of automata, and how it can be used in system validation. Dive into the world of formal languages, automata, and logic, and learn how they can be used to solve real-world problems.

Key Learning Points

Understand the basic concepts of automata theory and its applications in system validation
Learn how to design and analyze automata-based models
Explore the use of formal languages, automata, and logic in solving real-world problems

Learning Outcomes

Design and analyze automata-based models
Apply automata theory to solve real-world problems
Understand the relevance of formal languages, automata, and logic in computer science

Prerequisites or good to have knowledge before taking this course

Basic knowledge of programming
Familiarity with mathematical concepts

Course Difficulty Level

Intermediate

Course Format

Online self-paced
Video lectures
Quizzes and assignments

Similar Courses

Introduction to Formal Concept Analysis and Its Applications
Automata Theory

Related Education Paths

Notable People in This Field

Michael Sipser
Dexter Kozen

Related Books

Description

Have you ever experienced software systems failing? Websites crash, calendar not synchronising, or even a power blackout. Of course you have! But did you know that many of these errors are the result of communication errors either within a system or between systems? Depending on the system, the impact of software failures can be huge, even resulting in massive economic damage or loss of lives. Software, and in particular the communication between software-intensive systems, is very complex and very difficult to get right. However, we _need_ dependability in the systems we use, directly or indirectly, to support us in our everyday lives.

System Validation helps you to design embedded system behaviour that is structurally sound. It also enforces you to make the behaviour simple and insightful; systems that are designed for sound behaviour are also much easier to maintain and adapt. System Validation is the field that studies the fundamentals of system communication and information processing. The techniques put forward in system validaton allow to prove the absence of errors. This first course ’Automata and behavioural equivalences', builds the foundation of the subsequent courses, showing you how to look at system behaviour as state machines. It discusses behavioural equivalences and illustrate these in a number of examples and quizzes. This course explains labelled transition systems or automata to model behaviour for especially software controlled systems. An important question is when two behaviours represented by such automata are equal. The answer to this question is not at all straightforward, but the resulting equivalences are used as powerful tools to simplify complex behaviour. This allows us to exactly investigate and understand the behavioural properties of such systems precisely. Especially, in the combination with hiding of behaviour, equivalence reduction is a unique technique to obtain insight in the behaviour of systems, far more effective than simulation or testing. Using this insight we can make the models correct. Such models form an excellent basis for the production of concise, reliable and maintainable software. This course is part I of the set of courses for System Validation. System Validation, as a set of courses, is part of a larger EIT Digital online programme called 'Internet of Things through Embedded Systems'.

Outline

Behavioural modelling
Welcome
An automaton as a model for behaviour
Non-deterministic behaviour
The definition of an automaton
The wolf, the goat and the cabbage
Book exercises
Automata to model behaviour

Basic behavioural equivalences
Behavioural equivalences
Strong bisimulation
Trace equivalence
The internal or τ -action.
Branching bisimulation
Rooted branching bisimulation
Book exercises
Book exercises
Basic behavioural equivalences

More behavioural equivalences
The alternating bit protocol
Divergence preserving branching bisimulation
Weak trace equivalence
Weak bisimulation
Language, failure, and completed trace equivalence
When to use which behavioural equivalence
Transition systems with data, time and probabilities
More behavioural equivalences.

Summary of User Reviews

This course on Automata System Validation has received positive reviews overall, with many users praising the instructor's clear and concise teaching style. One key aspect that users found beneficial was the course's focus on real-world applications of automata theory.

Pros from User Reviews

Clear and concise teaching style
Real-world applications of automata theory
Challenging assignments that help solidify understanding
Great foundational course for further study in automata theory

Cons from User Reviews

Some users felt the pace was too fast
Not enough emphasis on certain topics
Limited interaction with other students
Lack of practical exercises

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