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The State of Hybrid Model-Based Testing. Michiel van Osch 21-06-2005. Index. Introduction Testing a Water Tank Controller Hybrid Model-Based Testing Conformance Relation Test-case generation Work in Progress Questions. ?“stop traffic”. ?“stop traffic”. !“red”. !“red”. pass.

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index
Index
  • Introduction
  • Testing a Water Tank Controller
  • Hybrid Model-Based Testing
    • Conformance Relation
    • Test-case generation
  • Work in Progress
  • Questions
model based testing

?“stop traffic”

?“stop traffic”

!“red”

!“red”

pass

Model-Based Testing

Test-tool

Discrete

Model

Discrete

System

hybrid systems

Hydrolic

pressure

Coffee with

Milk and Sugar

“brake”

“1”, “2”, “1”

Desired

Temperature: 25o

Room

Temperature

Hybrid Systems

ABS

hybrid model based testing

Lens

temperature

Lens

temperature

!”open

Cooling

Valve”

!”open

Cooling

Valve”

pass

Hybrid Model-based Testing

Test-tool

Hybrid-Model

Hybrid System

challenges
Challenges
  • Theory:
    • Develop Conformance Concepts
    • Develop Test-case Generation Algorithms
    • Prove Correctness and Applicability of Theory
  • Practice:
    • Implement Tooling
    • Exactly Model Relevant Aspects
    • Connect Models, Tools and Systems
index1
Index
  • Introduction
  • Testing a Water Tank Controller
  • Hybrid Model-Based Testing
    • Conformance Relation
    • Test-case generation
  • Work in Progress
  • Questions
the water tank controller
The water Tank Controller

set point

Tank Controller

messages

Water

Tank

Heater

Temperature

Sensor

Tank Controller

  • Discrete input: Set point
  • Discrete output: communication
  • Continuous input: Temperature

(from sensor)

  • Continuous output: Heat

(from Heater)

specification 1

Hybrid I/O

automaton

Specification (1)

Tank Controller

  • Discrete input: Set_setpoint(sp)
  • Discrete output: Print(“warning”)
  • Continuous input: ST
  • Continuous output: H
specification 2
Specification (2)

ST

H

ST

H

input

output

input

output

Heater OFF

Heater ON

test setup

Set_Setpoint(sp)

Set-point

ST

Temp. Sens.

Print(..)

Message

H

Heat

Test Setup

Tank Controller

Temperature

Sensor

Heater

Specification

Test-tool

Implementation

testing

Tank Controller

Temperature

Sensor

Heater

Testing...

Test-tool

Specification

Implementation

Temp. Sens.

ST

Heat

H

Specification

Implementation

testing1

Tank Controller

Temperature

Sensor

Heater

Temp. Sens.

ST

Heat

H

Testing…

Set_setpoint(SP)

Set-point

Test-tool

Specification

Implementation

Specification

Implementation

testing2

Tank Controller

Temperature

Sensor

Heater

Temp. Sens.

ST

Heat

H

Testing…

Test-tool

Specification

Implementation

Specification

Implementation

testing3

Tank Controller

Temperature

Sensor

Heater

Temp. Sens.

ST

Heat

H

Testing

fail

Print(“warning”)

“error”

Test-tool

Specification

Implementation

Specification

Implementation

testing4

Tank Controller

Temperature

Sensor

Heater

Temp. Sens.

ST

Heat

H

Testing…

fail

Test-tool

Specification

Implementation

Specification

Implementation

index2
Index
  • Introduction
  • Testing a Water Tank Controller
  • Hybrid Model-Based Testing
    • Conformance Relation
    • Test-case generation
  • Work in Progress
  • Questions
conformance
Conformance

A hybrid implementation is input-output conform a hybrid specification if for all observable traces of the specification:

The set of possible output actions and trajectories,

after the execution of a trace on the implementation,

is a subset of

the set of possible output actions or trajectories,

after the execution of a trace on the specification.

some decisions
Some Decisions
  • Defined on Hybrid I/O Automata
    • Input Action Enabled
    • Input Trajectory Enabled
    • Non-zeno
  • State Based: possible output actions and trajectories in a certain state
  • Input and output trajectories are treated together
  • There is no quiescence observation (as of yet)
conformance relation
Conformance relation

We Formally Define:

  • A hybrid trace  = 0 a11 a2 …as a sequence of discrete actions and trajectories of continuous variables (alternating)
  • A after : the set of states in which A can be after executing trace
  • out(q): the set of output actions or trajectories possible in state q
  • Out(Q): the set of output actions or trajectories possible in the set of states Q

Then implementation HIOA i is hiocospecification HIOAs if:

i hioco s if traces(s): out(i after )  out(s after )

examples
Examples

!a

!a

!c

Correct!

!b

!b

specification

implementation

Correct!

q

q

specification

implementation

examples1
Examples

!a

!a

!c

Incorrect!

!b

!b

specification

implementation

Incorrect!

q

q

specification

implementation

test case generation execution
Test-Case generation & Execution
  • Input actions: Select and stimulate
  • Output actions: Observe and validate
  • Trajectories:
    • Select a time up to which to apply input
    • Select an input trajectory to use for stimulation
    • Stimulate and observe output variables :
      • Until the end of the trajectory, without observing a mismatch between observed and specified output trajectories, in this case continue
      • Until an output action is observed, in this case validate the output action and if correct, then continue
      • Until a mismatch between observed and specified output variables occurs
  • As long as verdict “fail” is given, the verdict “pass” can be given
test case generation
Test-case generation

fail

?Set_setpoint(SP)

{SP > ST}

pass

fail

!Print(“error”)

!Print(“warning”)

pass

fail

index3
Index
  • Introduction
  • Testing a Water Tank Controller
  • Hybrid Model-Based Testing
    • Conformance Relation
    • Test-case generation
  • Work in Progress
  • Questions
work in progress 1

Coffee

temperature

“1”,”2”

When no coffee comes

out of the machine, temperature

Is not continuously 0!

While applying an input trajectory

and observing the output,

States change

q

q’

Work in Progress (1)
  • Does a continuous variable always have a value?
  • State Changes During a Trajectory
work in progress 2

What does this mean?

Work in Progress (2)
  • Quiescence
    • Is quiescence a property on the discrete actions of the system or also on continuous behavior of the system?
  • Notation
current future work
Current & Future Work
  • Further Develop these Concepts (Formalization, Theorems, Proofs)
  • Make Concepts Workable in Practice
    • Sampling of continuous behavior
    • Selecting Realistic Input Trajectories
    • Deal with Uncountable Many Possible Input and Output Trajectories and States
    • Deal with Inaccuracy of Observed Output
  • Implement Proof of Concept