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.
Overview
Syllabus
- 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.
- 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.
- 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.
- 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.
- Continuous Stochastic Logic
- 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.
Taught by
Anne Remke
