Laura Brand

1
A test generation framework for quiescent
real-time systems

• Laura Brandán Briones
• Dept. of CS, University of Twente, NL
• joint work with
• Ed Brinksma

2
Do We Still Need Quiescence?
Yes!
money?
money?
coffee!
tea !
coffee?
tea?
tea?
coffee?
bang?
bang?
coffee?
tea?
tea?
coffee?
coffee!
tea !
3
Do We Need Time?
Do We Need Coffee?
Do We Have Money?
Yes!
money?
money?
coffee!
coffee?
tea !
tea?
tea?
coffee?
x0
x0
x ? 6
x ? 6
4
Overview

• Real-time input-output transition systems
• Timed implementation relation
• Real-time test generation
• Example
• Future work (?)
• Multi real-time input-output transition systems
  
• Multi timed implementation relation
• Multi real-time test generation

5

• Real-time input-output transition systems

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non-delay actions are now assumed to occur
instantaneously

• LTS with delays
• s ? s (d?R) with
• (time determinism)
• s ? s and s ? s implies ss
• (density)
• s ? s iff ? s s ? s and s ?
  s with dd1d2
• (null delay)
• s ? s iff ss

?(d)
?(d)
?(d)
?(d1)
?(d2)
?(d)
?(0)
7

• Quiescence

8

• For a system p, we extend the time transition
  relation (?) with d (denoted ?(p))
• If for all o!?Lout q ?gt?,?
• q ? q

o!
d
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• Timed implementation relation

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• impl ?tiorf spec iff
• ttraces(?(impl)) ?
  ttraces(?(spec))
• impl ?tiorf spec iff ?M(impl) ? ?M(spec)
• where ?M(p) ttraces(?(p)) ? (D.L ?
  ?(M).d)

M
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• Outputs
• outM(s) o!(d) s gt ? d(M) s
  quiescent
• impl ? spec iff
• ?? outM( impl after ? ) ? outM( spec
  after ? )

o!(d)
tiocoM
M
tiorf
ioco
12

• Real-time test generation

13
Test cases
x 0
Test case t ? TTA TTA Test Timed Automata
x? k

, xk
on? x0
off!

• labels in L ? ? , G(d)
• tree-structured
• finite, deterministic
• final states pass and fail
• from each state ? pass, fail
• choose input i? and time k
• wait k accepting all outputs o! and
• at k provide input i?, or
• wait accepting all outputs o! and ?

fail
x?M
off! x5 x0
? xM
off! xlt5
x?M
fail
fail
?
off!
fail
pass
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Test Generation Algorithm (untimed)
ioco-sound conforming implementation not
rejected ioco-complete non-conforming
implementations rejected (in the limit)
Apply recursively non-deterministically (
initially S s0 )
15
Timed test generation
tiocoM-sound conforming implementation not
rejected tiocoM-complete non-conforming
implementations can be rejected
Apply recursively non-deterministically (
initially S s0 )
16

• Example

17
Example
test
c!
t!
m?
x1
fail
x0
fail
spec
t!
c!
d
c?
fail
x1
fail
x0
t!
c!
d
fail
xM
pass
x0
t!
c!
b?
fail
impl Mk
x1
fail
x0
t!
t!
c!
c?
fail
x1
fail
x0
c!
t!
d
xM
fail
pass
fail
18
Future work

• Extend the theory with multi input-output
• Confirm completeness (in the old sense)
• Evaluate applicability in practical situations
• Deal with the imprecision in measuring physical
  time
• Integrate with data testing

19
Overview

• Real-time input-output transition systems
• Timed implementation relation
• Real-time test generation
• Example
• Future work (?)
• Multi real-time input-output transition systems
  
• Multi timed implementation relation
• Multi real-time test generation

20
A generation framework for quiescent

test
real-time
multi input-output systems
input-output systems

• Laura Brandán Briones
• Ed Brinksma

21
amount!
card!
card?
card!
x 0
x gt 5
card!
x gt 5
Pin?
x 5
Err-P!
x 0
card!
t
x 5
x ? 5
t
Err-a!
x 5
Ok!
x 0
amount?
x 5
Ok!
x 0
x ? 5
t
t
x 5
x 5
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Channels
23

• Quiescence

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• L -quiescent (s)
• M quiescent (s)
• M quiescent (p)
• M-quiescent (p)

j
j
25
Channels
26

• Saturation

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2 1 2 3
? d d d
amount!
card!
card!
card?
x gt 5
x 0
card!
x gt 5
Pin?
x 5
Err-P!
1 1 2
x 0
? d d
card!
x ? 5
t
t
Err-a!
x 5
x 5
Ok!
x 0
1 1 2
1 1 2
? d d
? d d
d
amount?
x 5
Ok!
x 0
x ? 5
t
t
x 5
x 5
2 1 1 2
? ? d d
2 1 1 2
? ? d d
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a?.b!.c?.a?.b!
Ttraces
e(6).a?.e(3).b!.e(2).c?.e(1).a?.e(3).b!
e(6).a?.e(3).b!.e(2).c?.e(1).a?.e(3).b!
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(No Transcript)
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Outputs

• outM (s) U outM (s) U U outM (s)
• outM (s) o!(d) s gt
• U d (M ) j-quiescent(s gt)
• outM (s) U ? (d) i-refusal(s gt)

o
r
s?S
s?S
o
o!(d)
e(Mj)
j
j
e(d)
r
i
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1
M ltM1, M2, M3gtM1 1M2 1M3 2

• card! ? outM (s after card?(2).d
  (1).Pin?(2).Err-P!(3))
• outM (s after s) Ø ? s ? nttraces(s)

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Timed multi input-output implementation relation

• mtiocoM
• impl ?mtioco spec iff
• ?? outM (impl after ? ) ? outM (spec after ? )

M
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Test
mtiocoM-sound conforming implementation not
rejected mtiocoM-complete non-conforming
implementations can be rejected
Apply recursively non-deterministically (
initially S s0 )
34

• Future work

35

• Confirm completeness (in the old sense)
• Evaluate applicability in practical situations
• Deal with the imprecision in measuring physical
  time
• Integrate with data testing