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定量模型檢驗培訓

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.