Diagnosis, Synthesis and Analysis of Probabilistic Models
Diagnosis, Synthesis and Analysis of Probabilistic Models Tingting Han University of Twente, The Netherlands
September 25, 2009
Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
1/9
What do I do?
Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
2/9
What do I do?
Mom Fixing computers
Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
2/9
What do I do?
Mom Programming
Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
2/9
What do I do?
A college mate
Mom Applied mathematics, Formal methods
Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
2/9
What do I do?
A college mate
Mom
Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
2/9
What do I do?
A college mate
Mom
Han (University of Twente)
Correctness!
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
2/9
What do I do?
A college mate
Mom
Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
2/9
What do I do?
There should be no collisions! requirements
system
real−world Formalizing
formal−world
Modeling
A college mate
up to 107 states property specification
0.8 0.2
system model 0.6 0.4
¬collision Model Checking
Mom satisfied
violated
Counterexample state 1 state 2 state 3 state 4
0.678 0.9797 0.1523 0.2123
Model checking Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
2/9
What do I do?
A college mate
Mom
Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
2/9
What do I do?
A researcher in a workshop
A college mate
Mom add Probability!
Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
2/9
What do I do?
A researcher in a workshop
A college mate
Mom add Probability! ⇒ probabilistic model checking
Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
2/9
What do I do? Boss
A researcher in a workshop
A college mate
Mom
Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
2/9
Analysis
Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
3/9
Analysis
Specifications
Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
4/9
Analysis model z }| { How to model check CTMC against
? For CTMC model:
Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
4/9
Analysis specification model z }| { z }| { How to model check CTMC against linear real-time specification? For CTMC model:
Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
4/9
Analysis specification model z }| { z }| { How to model check CTMC against linear real-time specification? For CTMC model:
CTMC =⇒ probabilistic model checking ⇐= deterministic timed automata Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
4/9
Diagnosis
Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
5/9
Diagnosis
What’s wrong with your model?
Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
6/9
Diagnosis What’s wrong with your model?
Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
6/9
Diagnosis What’s wrong with your model?
Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
6/9
Diagnosis What’s wrong with your model?
What has been done? – Define a counterexample
Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
6/9
Diagnosis What’s wrong with your model?
What has been done? – Define a counterexample
Han (University of Twente)
– Design algorithms
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
6/9
Diagnosis What’s wrong with your model? Compact representation Before:
What has been done? – Define a counterexample – Compact representation Han (University of Twente)
After:
– Design algorithms
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
6/9
Diagnosis What’s wrong with your model?
What has been done? – Define a counterexample – Compact representation Han (University of Twente)
– Design algorithms – Generalization
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
6/9
Synthesis
Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
7/9
Synthesis
What parameter values can make the model “safe”?
Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
8/9
Synthesis What parameter values can make the model “safe”? trains[speed =?, length =?] satisfies P>0.9999 (no collision)
Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
8/9
Synthesis What parameter values can make the model “safe”? trains[speed =?, length =?] satisfies P>0.9999 (no collision)
Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
8/9
Synthesis What parameter values can make the model “safe”? trains[speed =?, length =?] satisfies P>0.9999 (no collision)
Parameter synthesis is much harder than model checking! Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
8/9
Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
9/9
September 25, 2009
Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
1/9
What do I do?
Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
2/9
What do I do?
Mom Fixing computers
Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
2/9
What do I do?
Mom Programming
Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
2/9
What do I do?
A college mate
Mom Applied mathematics, Formal methods
Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
2/9
What do I do?
A college mate
Mom
Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
2/9
What do I do?
A college mate
Mom
Han (University of Twente)
Correctness!
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
2/9
What do I do?
A college mate
Mom
Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
2/9
What do I do?
There should be no collisions! requirements
system
real−world Formalizing
formal−world
Modeling
A college mate
up to 107 states property specification
0.8 0.2
system model 0.6 0.4
¬collision Model Checking
Mom satisfied
violated
Counterexample state 1 state 2 state 3 state 4
0.678 0.9797 0.1523 0.2123
Model checking Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
2/9
What do I do?
A college mate
Mom
Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
2/9
What do I do?
A researcher in a workshop
A college mate
Mom add Probability!
Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
2/9
What do I do?
A researcher in a workshop
A college mate
Mom add Probability! ⇒ probabilistic model checking
Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
2/9
What do I do? Boss
A researcher in a workshop
A college mate
Mom
Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
2/9
Analysis
Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
3/9
Analysis
Specifications
Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
4/9
Analysis model z }| { How to model check CTMC against
? For CTMC model:
Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
4/9
Analysis specification model z }| { z }| { How to model check CTMC against linear real-time specification? For CTMC model:
Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
4/9
Analysis specification model z }| { z }| { How to model check CTMC against linear real-time specification? For CTMC model:
CTMC =⇒ probabilistic model checking ⇐= deterministic timed automata Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
4/9
Diagnosis
Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
5/9
Diagnosis
What’s wrong with your model?
Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
6/9
Diagnosis What’s wrong with your model?
Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
6/9
Diagnosis What’s wrong with your model?
Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
6/9
Diagnosis What’s wrong with your model?
What has been done? – Define a counterexample
Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
6/9
Diagnosis What’s wrong with your model?
What has been done? – Define a counterexample
Han (University of Twente)
– Design algorithms
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
6/9
Diagnosis What’s wrong with your model? Compact representation Before:
What has been done? – Define a counterexample – Compact representation Han (University of Twente)
After:
– Design algorithms
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
6/9
Diagnosis What’s wrong with your model?
What has been done? – Define a counterexample – Compact representation Han (University of Twente)
– Design algorithms – Generalization
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
6/9
Synthesis
Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
7/9
Synthesis
What parameter values can make the model “safe”?
Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
8/9
Synthesis What parameter values can make the model “safe”? trains[speed =?, length =?] satisfies P>0.9999 (no collision)
Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
8/9
Synthesis What parameter values can make the model “safe”? trains[speed =?, length =?] satisfies P>0.9999 (no collision)
Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
8/9
Synthesis What parameter values can make the model “safe”? trains[speed =?, length =?] satisfies P>0.9999 (no collision)
Parameter synthesis is much harder than model checking! Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
8/9
Han (University of Twente)
Diagnosis, Synthesis & Analysis of Probabilistic Models
Sept. 25, 2009
9/9
