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Quantitative Model Checking

Quantitative Model Checking

Instructor: Anne Remke

6,595 already enrolled

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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

What you'll learn

Learn the foundations of quantitative model checking for probabilistic and stochastic systems.
Model and analyse systems using Discrete-Time and Continuous-Time Markov Chains.
Apply Computational Tree Logic (CTL) and Probabilistic CTL (PCTL) to formally verify system properties.
Use formal verification techniques to evaluate the reliability, performance, and dependability of embedded, cyber-physical and communication systems

Skills you'll gain

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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.

Module details

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 videosTotal 61 minutes

Welcome!1 minute
Introduction13 minutes
Semantics of CTL13 minutes
Model Checking CTL10 minutes
The Until Operator13 minutes
The Always Operator10 minutes

3 readingsTotal 40 minutes

Script 1 and 2.110 minutes
Script 2.2 and 2.310 minutes
Script 2.420 minutes

4 assignmentsTotal 120 minutes

Check your understanding of CTL30 minutes
Formulate for yourself30 minutes
Test your understanding of CTL semantics30 minutes
Model checking eventually, always and until30 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 videosTotal 49 minutes

Introduction to DTMCs8 minutes
Evolution in Time13 minutes
Transient probabilities10 minutes
State classification6 minutes
Steady-state probabilities12 minutes

2 readingsTotal 20 minutes

Script 3.1 and 3.210 minutes
Script 3.310 minutes

5 assignmentsTotal 130 minutes

Compute transient probabilities10 minutes
State classification30 minutes
Steady-state computation30 minutes
Evolution of DTMCs30 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 videosTotal 36 minutes

Syntax of PCTL9 minutes
Model checking and the Next operator8 minutes
Time-bounded Until7 minutes
Backwards computation4 minutes
Unbounded Until9 minutes

3 readingsTotal 45 minutes

Script: 4.1 and 4.210 minutes
Script: 4.3.1 and 4.3.225 minutes
Script 4.3.310 minutes

6 assignmentsTotal 50 minutes

Checking PCTL next4 minutes
Checking time-bounded until16 minutes
Checking unbounded until10 minutes
PCTL Syntax8 minutes
Test your understanding of PCTL Until6 minutes
Test your understanding of PCTL6 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 videosTotal 56 minutes

Definition of a CTMC10 minutes
Generator matrix11 minutes
Steady-state probabilities11 minutes
Triple Modular Redundancy11 minutes
Uniformisation13 minutes

2 readingsTotal 35 minutes

Script: 5.1 and 5.220 minutes
Script: 5.315 minutes

6 assignmentsTotal 52 minutes

Test your understanding of CTMCs6 minutes
Steady state probability in CTMCs10 minutes
Test your understanding of Uniformisation6 minutes
Generator matrix6 minutes
Identifying BSCCs12 minutes
Uniformisation12 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.