Об этом курсе
4.3
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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....
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Approx. 20 hours to complete

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Approx. 20 hours to complete

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Программа курса: что вы изучите

Week
1
Clock
3 ч. на завершение

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. ...
Reading
6 видео (всего 61 мин.), 3 материалов для самостоятельного изучения, 4 тестов
Video6 видео
Welcome!1мин
Introduction13мин
Semantics of CTL13мин
Model Checking CTL9мин
The Until Operator12мин
The Always Operator9мин
Reading3 материала для самостоятельного изучения
Script 1 and 2.110мин
Script 2.2 and 2.310мин
Script 2.420мин
Quiz4 практического упражнения
Formulate for yourself6мин
Test your understanding of CTL semantics14мин
Check your understanding of CTL20мин
Model checking eventually, always and until22мин
Week
2
Clock
2 ч. на завершение

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. ...
Reading
5 видео (всего 49 мин.), 2 материалов для самостоятельного изучения, 5 тестов
Video5 видео
Evolution in Time13мин
Transient probabilities9мин
State classification5мин
Steady-state probabilities12мин
Reading2 материала для самостоятельного изучения
Script 3.1 and 3.210мин
Script 3.310мин
Quiz5 практического упражнения
Evolution of DTMCs6мин
Compute transient probabilities10мин
Classification of DTMC states True or False?14мин
State classification16мин
Steady-state computation12мин
Week
3
Clock
2 ч. на завершение

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. ...
Reading
5 видео (всего 36 мин.), 3 материалов для самостоятельного изучения, 6 тестов
Video5 видео
Model checking and the Next operator7мин
Time-bounded Until6мин
Backwards computation4мин
Unbounded Until8мин
Reading3 материала для самостоятельного изучения
Script: 4.1 and 4.210мин
Script: 4.3.1 and 4.3.225мин
Script 4.3.310мин
Quiz6 практического упражнения
PCTL Syntax8мин
Checking PCTL next4мин
Test your understanding of PCTL Until6мин
Checking time-bounded until16мин
Checking unbounded until10мин
Test your understanding of PCTL6мин
Week
4
Clock
2 ч. на завершение

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. ...
Reading
5 видео (всего 57 мин.), 2 материалов для самостоятельного изучения, 6 тестов
Video5 видео
Generator matrix11мин
Steady-state probabilities11мин
Triple Modular Redundancy11мин
Uniformisation12мин
Reading2 материала для самостоятельного изучения
Script: 5.1 and 5.220мин
Script: 5.315мин
Quiz6 практического упражнения
Generator matrix6мин
Test your understanding of CTMCs6мин
Steady state probability in CTMCs10мин
Identifying BSCCs12мин
Test your understanding of Uniformisation6мин
Uniformisation12мин

Преподаватель

Anne Remke

Prof. dr.
Computer Science

О EIT Digital

EIT Digital is a pan-European education and research-based open innovation organization founded on excellence. Its mission is to foster digital technology innovation and entrepreneurial talent for economic growth and quality of life. By linking education, research and business, EIT Digital empowers digital top talents for the future. EIT Digital provides online "blended" Innovation and Entrepreneurship education to raise quality, increase diversity and availability of the top-level content provided by 20 reputable universities of technology around Europe. The universities all together deliver a unique blend of the best of technical excellence and entrepreneurial skills and mindset to digital engineers and entrepreneurs at all stages of their careers. The academic partners support Coursera’s bold vision to enable anyone, anywhere, to transform their lives by accessing the world’s best learning experience. This means that EIT Digital gradually shares parts of its entrepreneurial and academic education programmes to demonstrate its excellence and make it accessible to a much wider audience. EIT Digital’s online education portfolio can be used as part of blended education settings, in both Master and Doctorate programmes, and for professionals as a way to update their knowledge. EIT Digital offers an online programme in 'Internet of Things through Embedded Systems'. Achieving all certificates of the online courses and the specialization provides an opportunity to enroll in the on campus program and get a double degree. These are the courses in the online programme: ...

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