Quantitative Model Checking
提供方
Quantitative Model Checking
EIT Digital
课程信息
4.3
23 个评分
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.
教学大纲 - 您将从这门课程中学到什么
Week
1Module 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 个视频（共 61 分钟）, 3 个阅读材料, 4 个测验
6 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
3 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
4 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
2Discrete 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 个视频（共 49 分钟）, 2 个阅读材料, 5 个测验
5 个视频
Evolution in Time13分钟
Transient probabilities9分钟
State classification5分钟
Steady-state probabilities12分钟
2 个阅读材料
Script 3.1 and 3.210分钟
Script 3.310分钟
5 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
3Probabilistic 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 个视频（共 36 分钟）, 3 个阅读材料, 6 个测验
5 个视频
Model checking and the Next operator7分钟
Time-bounded Until6分钟
Backwards computation4分钟
Unbounded Until8分钟
3 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
6 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
4Continuous 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 个视频（共 57 分钟）, 2 个阅读材料, 6 个测验
5 个视频
Generator matrix11分钟
Steady-state probabilities11分钟
Triple Modular Redundancy11分钟
Uniformisation12分钟
2 个阅读材料
Script: 5.1 and 5.220分钟
Script: 5.315分钟
6 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
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