## Oral Exam Questions

This page contains a list of question related to the course "Advanced Discrete Modelling". These questions are intended to help students check that they have understood the material in the theoretical and practical classes.

Furthermore, the exam will also be based on these questions, although this does *not* imply that the exam will be exclusively composed of the questions listed below. In addition, we will ask questions based on your assignment and your solutions.

**Discrete-Time Markov Chains (DTMCs)**

- What is a DTMC?
- Give an example of a DTMC
- How are DTMCs described mathematically / graphically?
- Draw a DTMC that describes the amount of money that a roulette player has assuming that he always bets one dollar on even.
- How are DTMCs simulated/solved?
- What types of solutions are there?
- What is a steady-state solution? Does every DTMC have one?
- What is an absorbing state?
- What does “memoryless” mean?
- Explain Google's pagerank computation

**Continuous-Time Markov Chains (CTMCs)**

- What is a CTMC?
- Give an example of a CTMC
- How are CTMCs described mathematically?
- What are similarities and differences to DTMCs?
- What is the connection to DTMCs?
- Give an intuitive explanation of the CTMC equations
- Explain the "dual" (i.e. discrete-time and continuous-time) views of a CTMC
- What is the connection between the exponential distribution and CTMCs?
- Explain why the exponential distribution is "memoryless"

**GSPNs and CTMCs**

- What is a GSPN?
- What is a reachability graph?
- What is the state space of a GSPN?
- What are vanishing and tangible markings?
- What is the connection between GSPNs and CTMCs?
- What are the advantages and disadvantages of discrete event simulation of a GSPN compared to setting up and solving its CTMC?
- Draw the GSPN of a simple Service process with one queue
- Demonstrate how to turn a given GSPN into a CTMC

**Proxels**

- What is a proxel?
- What information does the proxel carry?
- How are proxels used to analyse an SPN?
- What are the main properties of the proxel-based simulation?
- What influence does the time step have?
- For which models is the proxel-based simulation especially suitable?
- Draw an example Proxel tree
- What is the formula and meaning of the HRF/IRF?

**Hidden Markov Models**

- What are the elements of a Hidden Markov Model?
- What are the three basic problems that one can solve using a HMM?
- What is a typical example of a HMM?
- What Question does the Evaluation (Decoding, Training) problem solve? How can it be solved?
- What are practical applications of Evaluation and Training?

**Hidden non-Markovian Models**

- What is the motivation behind combining SPNs and HMMs? Practical example?
- How would you extend the definition of a Proxel to do path & output sequence analysis?
- What are the differences / similarities between HMM and HnMM?

**Solving HnMM**

- How could you use the Proxel-based simulation algorithm to analyze (evaluation and decoding) Hidden non-Markovian Models?
- What are pitfalls?
- What problems did you encounter?
- How can DPH be used to train Hidden non-Markovian Models? (Idea)