Quantitative Model Checking

Quantitative Model Checking

Instructor: Anne Remke

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5 modules

Gain insight into a topic and learn the fundamentals.

54 reviews

Intermediate level

Some related experience required

1 week to complete

at 10 hours a week

Flexible schedule

Learn at your own pace

5 modules

Gain insight into a topic and learn the fundamentals.

54 reviews

Intermediate level

Some related experience required

1 week to complete

at 10 hours a week

Flexible schedule

Learn at your own pace

Skills you'll gain

Details to know

Shareable certificate

Add to your LinkedIn profile

Assessments

27 assignments

Taught in English

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There are 5 modules in this course

Welcome to the cutting-edge course on Quantitative Model Checking for Markov Chains! As technology permeates every aspect of modern life—Embedded Systems, Cyber-Physical Systems, Communication Protocols, and Transportation Systems—the need for dependable software is at an all-time high. One tiny flaw can lead to catastrophic failures and enormous costs. That's where you come in.

The course kicks off with creating a State Transition System, the basic model that captures the intricate dynamics of real-world systems. Soon you'll step into the world of Discrete-time and Continuous-time Markov Chains—powerful mathematical formalisms that are versatile enough to model complex systems yet elegant in their design. These aren't just theories; they are tools actively used across various domains for performance and dependability evaluation. But we won't stop at modelling. The heart of this course is 'Model Checking,' a formal verification method that scrutinizes the functionality of your system model. Learn how to express dependability properties, track the evolution of Markov chains over time, and verify whether states meet particular conditions—all using advanced computational algorithms. By the end of this course, you'll be equipped with the skills to: - Specify dependability properties for a range of transition systems. - Understand the temporal evolution of Markov chains. - Analyze and compute the satisfaction set for multiple properties. Are you ready to become an expert in ensuring the reliability of tomorrow's technologies? Click here to Enroll today and join us in mastering the art and science of model checking.

We introduce Labeled Transition Systems (LTS), the syntax and semantics of Computational Tree Logic (CTL) and discuss the model checking algorithms that are necessary to compute the satisfaction set for specific CTL formulas.

What's included

6 videos3 readings4 assignments

6 videos Total 61 minutes

Welcome! 1 minute
Introduction 13 minutes
Semantics of CTL 13 minutes
Model Checking CTL 10 minutes
The Until Operator 13 minutes
The Always Operator 10 minutes

3 readings Total 40 minutes

Script 1 and 2.1 10 minutes
Script 2.2 and 2.3 10 minutes
Script 2.4 20 minutes

4 assignments Total 120 minutes

Formulate for yourself 30 minutes
Test your understanding of CTL semantics 30 minutes
Model checking eventually, always and until 30 minutes
Check your understanding of CTL 30 minutes

We enhance transition systems by discrete time and add probabilities to transitions to model probabilistic choices. We discuss important properties of DTMCs, such as the memoryless property and time-homogeneity. State classification can be used to determine the existence of the limiting and / or stationary distribution.

What's included

5 videos2 readings5 assignments

5 videos Total 49 minutes

Introduction to DTMCs 8 minutes
Evolution in Time 13 minutes
Transient probabilities 10 minutes
State classification 6 minutes
Steady-state probabilities 12 minutes

2 readings Total 20 minutes

Script 3.1 and 3.2 10 minutes
Script 3.3 10 minutes

5 assignments Total 130 minutes

Compute transient probabilities 10 minutes
State classification 30 minutes
Steady-state computation 30 minutes
Evolution of DTMCs 30 minutes
Classification of DTMC states True or False? 30 minutes

We discuss the syntax and semantics of Probabilistic Computational Tree logic and check out the model checking algorithms that are necessary to decide the validity of different kinds of PCTL formulas. We shortly discuss the complexity of PCTL model checking.

What's included

5 videos3 readings6 assignments

5 videos Total 36 minutes

Syntax of PCTL 9 minutes
Model checking and the Next operator 8 minutes
Time-bounded Until 7 minutes
Backwards computation 4 minutes
Unbounded Until 9 minutes

3 readings Total 45 minutes

Script: 4.1 and 4.2 10 minutes
Script: 4.3.1 and 4.3.2 25 minutes
Script 4.3.3 10 minutes

6 assignments Total 50 minutes

Checking PCTL next 4 minutes
Checking time-bounded until 16 minutes
Checking unbounded until 10 minutes
PCTL Syntax 8 minutes
Test your understanding of PCTL Until 6 minutes
Test your understanding of PCTL 6 minutes

We enhance Discrete-Time Markov Chains with real time and discuss how the resulting modelling formalism evolves over time. We compute the steady-state for different kinds of CMTCs and discuss how the transient probabilities can be efficiently computed using a method called uniformisation.

What's included

5 videos2 readings6 assignments

5 videos Total 56 minutes

Definition of a CTMC 10 minutes
Generator matrix 11 minutes
Steady-state probabilities 11 minutes
Triple Modular Redundancy 11 minutes
Uniformisation 13 minutes

2 readings Total 35 minutes

Script: 5.1 and 5.2 20 minutes
Script: 5.3 15 minutes

6 assignments Total 52 minutes

Generator matrix 6 minutes
Identifying BSCCs 12 minutes
Uniformisation 12 minutes
Test your understanding of CTMCs 6 minutes
Steady state probability in CTMCs 10 minutes
Test your understanding of Uniformisation 6 minutes

We introduce the syntax and semantics of Continuous Stochastic Logic and describe how the different kinds of CSL formulas can be model checked. Especially, model checking the time bounded until operator requires applying the concept of uniformisation, which we have discussed in the previous module.