Clocks, Dice and ProcessesClocks, Dice and Processes

PhD Promotion September 21, 2009PhD Promotion September 21, 2009

Taolue Chen

Vrije Universiteit Amsterdam, The Vrije Universiteit Amsterdam, The NetherlandsNetherlands

CoverCover

Context of PhD workContext of PhD work

General goal of the research:General goal of the research:

Make ICT systems Make ICT systems correctcorrect!!

How?How?

We apply mathematics – We apply mathematics – Formal Formal methodsmethods

Concurrency theoryConcurrency theory

ModelingModeling and and verificationverification of of concurrent systems.concurrent systems.

Theoretical Theoretical questionsquestions

This dissertationThis dissertation

ModelModel |=|= Specification SpecificationFormal world

Real world SystemSystem “meets”“meets” Requirement Requirement

aroundaround

What models?What models?

AutomataAutomata-based models-based models

e.g. finite-state machine; labeled e.g. finite-state machine; labeled transition system; Kripke structure …transition system; Kripke structure …

states and transitions of an Automatic Pilot

What models?What models?

LanguageLanguage-based models-based models

e.g. process algebra, LOTOS …e.g. process algebra, LOTOS …

AutomataAutomata-based specifications-based specifications

LogicLogic-based specifications-based specifications, e.g. , e.g.

What specifications?What specifications?

2

1

reqack≈≈

■■(req (req ◆ ack) ◆ ack)

How to verify?How to verify?

Deductive approachDeductive approach Enumerative Enumerative approachapproach

Theorem proverTheorem prover Model Model checkerchecker

ModelModel |=|= Specification Specification??Formal

statement

This dissertation – This dissertation – Part I: Axiomatization of Process Part I: Axiomatization of Process

AlgebraAlgebra

Basic questionsBasic questions on on deductivedeductive approaches approaches for for language-basedlanguage-based models. models.

Part II: Verification of Probabilistic Part II: Verification of Probabilistic Real-time SystemsReal-time Systems

AlgorithmsAlgorithms on on enumerativeenumerative approaches for approaches for automata-basedautomata-based models. models.

Part I: Axiomatization of Process Part I: Axiomatization of Process AlgebraAlgebra

Basic questionsBasic questions on on deductivedeductive approaches approaches for for language-basedlanguage-based models. models.

Part II: Verification of Probabilistic Part II: Verification of Probabilistic Real-time SystemsReal-time Systems

AlgorithmsAlgorithms on on enumerativeenumerative approaches for approaches for automata-basedautomata-based models. models.

In In processprocess algebra, algebra,

ModelModel ≈ SpecificationSpecification

Part I: Axiomatization of PAPart I: Axiomatization of PA

For each equivalence or preorder,For each equivalence or preorder, does it afford a finite (ground- or does it afford a finite (ground- or ωω-) -) complete axiomatization?complete axiomatization?

Crucial!

But there are But there are hundredshundreds of different equivalences of different equivalences and preorders! We need and preorders! We need INSIGHTINSIGHT into them! into them!

Embedded applications feature systems exhibEmbedded applications feature systems exhibiting both and behaviors.iting both and behaviors.

Modeled by advanced stochastic Modeled by advanced stochastic processes:processes:

Part II: Verification of Part II: Verification of probabilistic real-time systemsprobabilistic 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

Thank you!Thank you!

and to