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Quantitative Model Checking

Approx. 18 hours to complete

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Course Summary

Learn the fundamental concepts and techniques of quantitative model checking, an automated method for verifying and validating complex systems.

Key Learning Points

Gain knowledge of quantitative model checking concepts and techniques
Learn how to apply quantitative model checking to real-world problems
Understand the limitations and challenges of quantitative model checking

Learning Outcomes

Understand the principles and techniques of quantitative model checking
Be able to apply quantitative model checking to real-world problems
Gain insights into the limitations and challenges of quantitative model checking

Prerequisites or good to have knowledge before taking this course

Basic knowledge of probability and statistics
Familiarity with programming languages such as C or Python

Course Difficulty Level

Intermediate

Course Format

Self-paced
Online
Video lectures

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Formal Verification
Model Checking

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Description

The integration of ICT (information and communications technology) in different applications is rapidly increasing in e.g. Embedded and Cyber physical systems, Communication protocols and Transportation systems. Hence, their reliability and dependability increasingly depends on software. Defects can be fatal and extremely costly (with regards to mass-production of products and safety-critical systems).

First, a model of the real system has to be built. In the simplest case, the model reflects all possible states that the system can reach and all possible transitions between states in a (labelled) State Transition System. When adding probabilities and discrete time to the model, we are dealing with so-called Discrete-time Markov chains which in turn can be extended with continuous timing to Continuous-time Markov chains. Both formalisms have been used widely for modeling and performance and dependability evaluation of computer and communication systems in a wide variety of domains. These formalisms are well understood, mathematically attractive while at the same time flexible enough to model complex systems. Model checking focuses on the qualitative evaluation of the model. As formal verification method, model checking analyzes the functionality of the system model. A property that needs to be analyzed has to be specified in a logic with consistent syntax and semantics. For every state of the model, it is then checked whether the property is valid or not. The main focus of this course is on quantitative model checking for Markov chains, for which we will discuss efficient computational algorithms. The learning objectives of this course are as follows: - Express dependability properties for different kinds of transition systems . - Compute the evolution over time for Markov chains. - Check whether single states satisfy a certain formula and compute the satisfaction set for properties.

Outline

Module 1: Computational Tree Logic
Welcome!
Introduction
Semantics of CTL
Model Checking CTL
The Until Operator
The Always Operator
Script 1 and 2.1
Script 2.2 and 2.3
Script 2.4
Formulate for yourself
Test your understanding of CTL semantics
Check your understanding of CTL
Model checking eventually, always and until

Discrete Time Markov Chains
Introduction to DTMCs
Evolution in Time
Transient probabilities
State classification
Steady-state probabilities
Script 3.1 and 3.2
Script 3.3
Evolution of DTMCs
Compute transient probabilities
Classification of DTMC states True or False?
State classification
Steady-state computation

Probabilistic Computational Tree Logic
Syntax of PCTL
Model checking and the Next operator
Time-bounded Until
Backwards computation
Unbounded Until
Script: 4.1 and 4.2
Script: 4.3.1 and 4.3.2
Script 4.3.3
PCTL Syntax
Checking PCTL next
Test your understanding of PCTL Until
Checking time-bounded until
Checking unbounded until
Test your understanding of PCTL

Continuous Time Markov Chains
Definition of a CTMC
Generator matrix
Steady-state probabilities
Triple Modular Redundancy
Uniformisation
Script: 5.1 and 5.2
Script: 5.3
Generator matrix
Test your understanding of CTMCs
Steady state probability in CTMCs
Identifying BSCCs
Test your understanding of Uniformisation
Uniformisation

Continuous Stochastic Logic
Model checking CSL
Model checking and Time-bounded next
Model checking the steady-state operator
Time-bounded Until
An application
Script: 6.1
Script: 6.2
Assembly line
Test your understanding of CSL (I)
Steady state and next
Test your understanding of CSL (II)
Time bounded until in CSL
Test your understanding of CSL (III)

Summary of User Reviews

The Quantitative Model Checking course on Coursera has received positive reviews from users. Many found the course to be informative and well-structured, with a focus on practical applications. Overall, the course has received high ratings from users.

Key Aspect Users Liked About This Course

The course is well-structured and focuses on practical applications.

Pros from User Reviews

The course provides a comprehensive overview of quantitative model checking
The instructors are knowledgeable and engaging
The course is well-paced and easy to follow
The assignments and quizzes are helpful for reinforcing concepts
The course provides practical examples and applications

Cons from User Reviews

Some users found the course to be too technical
The course requires a strong background in mathematics and computer science
The course may not be suitable for beginners
Some users found the lectures to be too long and dense
The course may require a significant time commitment

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