1. Clocks, Dice and Processes PhD Promotion September 21, 2009 Taolue Chen Vrije Universiteit Amsterdam, The Netherlands

2. Cover

3. Context of PhD work General goal of the research: Make ICT systems correct!

4. How? We apply mathematics – Formal methods

5. Concurrency theory Modeling and verification of concurrent systems. Modeling and verification of concurrent systems.

6. Theoreticalquestions This dissertation Model |= Specification Formal world Real world System “ meets ” Requirement around

7. What models? Automata-based models e.g. finite-state machine; labeled transition system; Kripke structure … e.g. finite-state machine; labeled transition system; Kripke structure … states and transitions of an Automatic Pilot

8. What models? Language-based models e.g. process algebra, LOTOS … e.g. process algebra, LOTOS …

9. Automata-based specifications Automata-based specifications Logic-based specifications, e.g. Logic-based specifications, e.g. What specifications? 2 1 reqack ≈ ■ (req  ◆ ack)

10. How to verify? Deductive approach Enumerative approach Theorem prover Model checker Theorem prover Model checker Model |= Specification? Formal statement

11. This dissertation – Part I: Axiomatization of Process Algebra Part I: Axiomatization of Process Algebra Basic questions on deductive approaches for language-based models. Basic questions on deductive approaches for language-based models. Part II: Verification of Probabilistic Real- time Systems Part II: Verification of Probabilistic Real- time Systems Algorithms on enumerative approaches for automata-based models. Algorithms on enumerative approaches for automata-based models. Part I: Axiomatization of Process Algebra Part I: Axiomatization of Process Algebra Basic questions on deductive approaches for language-based models. Basic questions on deductive approaches for language-based models. Part II: Verification of Probabilistic Real- time Systems Part II: Verification of Probabilistic Real- time Systems Algorithms on enumerative approaches for automata-based models. Algorithms on enumerative approaches for automata-based models.

12. In process algebra, Model Specification Model ≈ Specification Part I: Axiomatization of PA For each equivalence or preorder, For each equivalence or preorder, does it afford a finite (ground- or ω -) does it afford a finite (ground- or ω -) complete axiomatization? complete axiomatization? Crucia l ! But there are hundreds of different equivalences and preorders! We need INSIGHT into them!

13. Embedded applications feature systems exhibiting both and behaviors. Embedded applications feature systems exhibiting both and behaviors. Modeled by advanced stochastic processes: Modeled by advanced stochastic processes: Part II: Verification of probabilistic real-time systems Continuous-time Markov chains Probabilistic timed automata … How to model check them and How to model check them and perform state space reduction? perform state space reduction? Piecewise determi- nistic processes

14. Thank you! and to