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#### 100% online

Start instantly and learn at your own schedule.

#### Approx. 21 hours to complete

Suggested: 5 weeks of study, each with around 2.h hours work...

#### English

Subtitles: English

#### 100% online

Start instantly and learn at your own schedule.

#### Approx. 21 hours to complete

Suggested: 5 weeks of study, each with around 2.h hours work...

#### English

Subtitles: English

### Syllabus - What you will learn from this course

Week
1
3 hours to complete

## Module 1: Computational Tree Logic

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. ...
6 videos (Total 61 min), 3 readings, 4 quizzes
6 videos
Introduction13m
Semantics of CTL13m
Model Checking CTL9m
The Until Operator12m
The Always Operator9m
Script 1 and 2.110m
Script 2.2 and 2.310m
Script 2.420m
4 practice exercises
Formulate for yourself6m
Test your understanding of CTL semantics14m
Model checking eventually, always and until22m
Week
2
2 hours to complete

## Discrete Time Markov Chains

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. ...
5 videos (Total 49 min), 2 readings, 5 quizzes
5 videos
Evolution in Time13m
Transient probabilities9m
State classification5m
Script 3.1 and 3.210m
Script 3.310m
5 practice exercises
Evolution of DTMCs6m
Compute transient probabilities10m
Classification of DTMC states True or False?14m
State classification16m
Week
3
2 hours to complete

## Probabilistic Computational Tree Logic

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. ...
5 videos (Total 36 min), 3 readings, 6 quizzes
5 videos
Model checking and the Next operator7m
Time-bounded Until6m
Backwards computation4m
Unbounded Until8m
Script: 4.1 and 4.210m
Script: 4.3.1 and 4.3.225m
Script 4.3.310m
6 practice exercises
PCTL Syntax8m
Checking PCTL next4m
Test your understanding of PCTL Until6m
Checking time-bounded until16m
Checking unbounded until10m
Week
4
2 hours to complete

## Continuous Time Markov Chains

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. ...
5 videos (Total 57 min), 2 readings, 6 quizzes
5 videos
Generator matrix11m
Triple Modular Redundancy11m
Uniformisation12m
Script: 5.1 and 5.220m
Script: 5.315m
6 practice exercises
Generator matrix6m
Identifying BSCCs12m
Uniformisation12m

Prof. dr.
Computer Science