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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
Context of PhD workContext of PhD work
General goal of the research:General goal of the research:
Make ICT systems Make ICT systems correctcorrect!!
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