课程信息
4.3
23 个评分
4 个审阅
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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Intermediate Level

中级

Clock

Approx. 20 hours to complete

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

100% 在线课程

立即开始,按照自己的计划学习。
Calendar

可灵活调整截止日期

根据您的日程表重置截止日期。
Intermediate Level

中级

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Approx. 20 hours to complete

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

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教学大纲 - 您将从这门课程中学到什么

Week
1
Clock
完成时间为 3 小时

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 个视频(共 61 分钟), 3 个阅读材料, 4 个测验
Video6 个视频
Welcome!1分钟
Introduction13分钟
Semantics of CTL13分钟
Model Checking CTL9分钟
The Until Operator12分钟
The Always Operator9分钟
Reading3 个阅读材料
Script 1 and 2.110分钟
Script 2.2 and 2.310分钟
Script 2.420分钟
Quiz4 个练习
Formulate for yourself6分钟
Test your understanding of CTL semantics14分钟
Check your understanding of CTL20分钟
Model checking eventually, always and until22分钟
Week
2
Clock
完成时间为 2 小时

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 个视频(共 49 分钟), 2 个阅读材料, 5 个测验
Video5 个视频
Evolution in Time13分钟
Transient probabilities9分钟
State classification5分钟
Steady-state probabilities12分钟
Reading2 个阅读材料
Script 3.1 and 3.210分钟
Script 3.310分钟
Quiz5 个练习
Evolution of DTMCs6分钟
Compute transient probabilities10分钟
Classification of DTMC states True or False?14分钟
State classification16分钟
Steady-state computation12分钟
Week
3
Clock
完成时间为 2 小时

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 个视频(共 36 分钟), 3 个阅读材料, 6 个测验
Video5 个视频
Model checking and the Next operator7分钟
Time-bounded Until6分钟
Backwards computation4分钟
Unbounded Until8分钟
Reading3 个阅读材料
Script: 4.1 and 4.210分钟
Script: 4.3.1 and 4.3.225分钟
Script 4.3.310分钟
Quiz6 个练习
PCTL Syntax8分钟
Checking PCTL next4分钟
Test your understanding of PCTL Until6分钟
Checking time-bounded until16分钟
Checking unbounded until10分钟
Test your understanding of PCTL6分钟
Week
4
Clock
完成时间为 2 小时

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 个视频(共 57 分钟), 2 个阅读材料, 6 个测验
Video5 个视频
Generator matrix11分钟
Steady-state probabilities11分钟
Triple Modular Redundancy11分钟
Uniformisation12分钟
Reading2 个阅读材料
Script: 5.1 and 5.220分钟
Script: 5.315分钟
Quiz6 个练习
Generator matrix6分钟
Test your understanding of CTMCs6分钟
Steady state probability in CTMCs10分钟
Identifying BSCCs12分钟
Test your understanding of Uniformisation6分钟
Uniformisation12分钟

讲师

Anne Remke

Prof. dr.
Computer Science

关于 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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