From last lecture
TDDC05: Embedded Systems
• How did the Mealy composition example
work out?
Simulation and Verification
Lecture 3: Modelling, synchronous
languages
Simin Nadjm-Tehrani
• Problems with definition of new
operators?
• This lecture: Wrapping up modelling…
Real-time Systems Laboratory
Department of Computer and Information Science
Embedded systems simulation and verification
Linköping university
21 pages
Spring term 2006
Earlier …
Embedded systems simulation and verification
Linköping university
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Spring term 2006
Example: functional model
Landing gear controller:
•
•
•
•
Architectural (component)
Functional (input - output)
Behavioural (over ”time”)
Non-functional
– dependability: reliability, safety,
availability, maintainability,...
– timeliness,
• Other (size, weight, shape, cost, ...)
Embedded systems simulation and verification
Linköping university
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Example: behavioural model
Closing
Opening
Idle
g2
– g3 ↔ closed ∨ [7] ∨ [4]
g8
g5
Extending
Embedded systems simulation and verification
Linköping university
• Where the guards (transition conditions) are:
– g2 ↔ (¬cmd ∧ ([8] ∨ [2])) ∨
(cmd ∧ ([9] ∨ [3]) )
g4
g6
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– g1 ↔ open ∨ [7] ∨ [1]
g3
g1
Embedded systems simulation and verification
Linköping university
– g4 ↔ (cmd ∧ ([8] ∨ [5])) ∨
(¬ cmd ∧ ([9] ∨ [6]) )
g7
Retracting
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– g5 ↔ out ∨ [9] ∨ [7]
...
Embedded systems simulation and verification
Linköping university
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• And where conditions [k] are given by:
Timed model
g1 [l, u]
– [2] ↔ ¬ open ∧ closed ∧ ¬in ∧ out
g8
g5
– [9] ↔ ¬ open ∧ ¬ closed ∧ in ∧ ¬ out
Parallelism
Communication between subsystems
Hierarchy
Timing
Data-flow/control-flow oriented
Discrete/continuous state
g7
Retracting
Extending
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Embedded systems simulation and verification
Linköping university
Expressiveness of language
Embedded systems simulation and verification
Linköping university
g4
g6
– [8] ↔ ¬ open ∧ ¬ closed ∧ ¬ in ∧ out
•
•
•
•
•
•
g3
Idle
g2
– [3] ↔ ¬ open ∧ closed ∧ in ∧ ¬ out
...
Embedded systems simulation and verification
Linköping university
Closing
Opening
– [1] ↔ ¬ open ∧ closed ∧ ¬in ∧ ¬out
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Discrete models
Example language/tool:
• Untimed, parallel, hierarchical,
synchronous
– State-based (control-flow):
Statecharts/STATEMATE
– Block diagrams (Data-flow):
Lustre/SCADE
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Statemate model
Embedded systems simulation and verification
Linköping university
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Simple example in Lustre
node Stopwatch (start-stop, reset, hs: bool)
returns (time: int; running: bool);
let
time = 0 -> if hs and running
then pre(time) + 1
else if reset
then 0
else pre(time);
running = false -> if start-stop
then not pre(running)
else pre(running);
tel
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Linköping university
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Embedded systems simulation and verification
Linköping university
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Reactive systems
• Conceptual notion
• C.f. transformational systems
that produce a result when the
execution terminates
• Reactive systems
maintain a continuous interaction with
their environments
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Linköping university
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Compare with feedback
• Consider a one-place buffer and a twoplace buffer as transformational
programs
• They are equivalent wrt the function
• Are they equivalent if their outputs are
fed in as inputs?
Embedded systems simulation and verification
Linköping university
Some desirable properties
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What is desirable here?
• Abstraction: do not fix time granularity
until very final stages of implementation
• Causality: an event should not be able
to trigger itself
Not A
/B
B/A
A/B
B/A
• Consistency: transitions taken in a step
are not disabled by parallel transitions
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Linköping university
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Embedded systems simulation and verification
Linköping university
Verification in Lustre
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Environment models
The bright side ☺
• Causality, determinism, consistency:
dealt with by the compiler
• Mode-automata combine automata
states (for modes) with Lustre (for data
flow in each mode)
• Connections to formal verification and
optimisation tools
Mathematical approximations
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Linköping university
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Linköping university
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Which environment?
Wrapping up: modelling
• Many formal and informal modelling
notations
• This course treats
– Informal notations for req. spec.
– Formal language for design spec.
• Lustre/SCADE
• With Mealy machines as underlying
semantics
– Formal language for spec. of static
reqs. (Next two lectures)
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Linköping university
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Future: Components
• Need not build from scratch
• Design flow is changed
Capture
Specify
Design
Implement
Find
Test
Select
Maintain
Adapt
Deploy
Compose
Replace
Embedded systems simulation and verification
Linköping university
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Embedded systems simulation and verification
Linköping university
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Spring term 2006