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?
tea !
coffee!
coffee?
tea?
tea?
coffee?
bang?
bang?
tea?
coffee?
coffee?
tea?
coffee!
tea !
June, 2005

3. Do We Need Time? Do We Have Money? Do We Need Coffee? Yes! money?
tea !
coffee?
coffee!
tea?
tea?
coffee?
x:=0
x:=0
x  6
x  6
June, 2005

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
June, 2005

5. Real-time input-output transition systems
June, 2005

6. occur instantaneously
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 s’=s’’
(density)
s  s’ iff  s’’ : s  s’’ and s’’  s’ with d=d1+d2
(null delay)
s  s’ iff s=s’
(d)
(d)
(d)
(d)
(d1)
(d2)
(0)
June, 2005

7. Quiescence
June, 2005

8. If for all o!Lout : q >, q  q
For a system p, we extend the time transition relation () with δ (denoted Δ(p)):
If for all o!Lout : q >,
q  q o! δ
June, 2005

9. Timed implementation relation
June, 2005

10. ttraces(Δ(impl))  ttraces(Δ(spec))
impl tiorf spec iff
ttraces(Δ(impl))  ttraces(Δ(spec))
impl tiorf spec iff ΔM(impl)  ΔM(spec)
where ΔM(p) = ttraces(Δ(p))  (D.L  (M).δ)* M
June, 2005

11. Outputs outM(s) = { o!(d) | s => }  { δ(M) | s quiescent}
impl  spec iff
 : outM( impl after  )  outM( spec after  )
o!(d)
tiocoM
(D.L  (M).δ) M
ΔM(spec)
tiorf
ioco
June, 2005

12. Real-time test generation
June, 2005

13. Test cases Test case t  TTA TTA – Test Timed Automata :
x:= 0
Test case t  TTA
TTA – Test Timed Automata :
x k
on?
x:=0
, x=k
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!
x=5
x:=0 
x=M
off!
x<5
xM
fail
fail 
off!
pass
fail
June, 2005

14. Timed test generation tiocoM-sound
= conforming implementation not rejected
tiocoM-complete
= non-conforming implementations can
be rejected
Apply recursively & non-deterministically ( initially S = {s0} )
1 end test case
PASS
allowed oj! after d time-units
2 choose k  (0, M) and input μ
FAIL
forbidden oi! after d’ time-units
o1!
x=dn
x=d1
x=d’n’
x=k
x  k tμ t1 tn
x:=0
x=d’1
on’! μ?
on!
allowed oj! after d time-units
3 wait to observe possible output
FAIL
forbidden oi! after d’ time-units 
x=d’1
x=dn
x=d1
x=d’n’
x=M
x  M tδ t1 tn
x:=0
o1!
on’!
on!
June, 2005

15. Example
June, 2005

16. Example :test spec: impl: fail fail δ fail fail fail pass fail failb? c! t!
x  1 c! t! δ c?
x=1
fail
fail
x:=0
x  M c! t! δ
pass
x=M
fail
x:=0
x  1 c! t! b?
impl:
M=k
x=1
fail
fail
x:=0 m? t? c? b? c!
x<k t!
x  1 c! t! c?
fail
fail
x=1
x:=0
x  M c! t! δ
x=M
pass
fail
fail
June, 2005

17. 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
June, 2005

18. 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
June, 2005

19. Laura Brandán Briones & Ed Brinksma
A generation framework for quiescent
test
real-time
multi input-output systems
input-output systems
Laura Brandán Briones
&
Ed Brinksma

20. amount! card! card? card! card! Pin? Err-P! card! τ τ Err-a! Ok!
x > 5
x := 0
card!
x > 5
Pin?
x ≤ 5
Err-P!
x := 0
card! τ
x ≤ 5
x  5
Err-a! τ
x ≤ 5
Ok!
x := 0
amount?
x ≤ 5
Ok!
x := 0
x  5 τ τ
x ≤ 5
x ≤ 5
June, 2005

21. Channels τ amount! card? L = { card?} Pin? L = { Pin?, amount?} Err-P!
Ok!
Pin?
Err-P!
card!
Err-a!
amount!
x5
x := 0
x ≤ 5 τ
amount?
x > 5
L = { card?} I 1
L = { Pin?, amount?} I 2 1 U
L = { card!} U
L = { amount!} 2
L = { Ok!, Err-a!, Err-P!} U 3
June, 2005

22. Quiescence
June, 2005

23. L -quiescent (s) M –quiescent (s) M –quiescent (p) M-quiescent (p) o!
o! Є L U j j U
L -quiescent (s)
M –quiescent (s)
M –quiescent (p)
M-quiescent (p) o! M j o! j M
o! Є L U j j o! M i u!
u! Є L U
o! Є L j
June, 2005

24. Channels τ card? Ok! Pin? Err-P! card! Err-a! amount! amount?
x5
x := 0
x ≤ 5 τ
amount?
x > 5
L = { card?} I 1
=> γ
L = { Pin?, amount?} I 2
=> γ 1 U
L = { card!}
=> δ U
L = { amount!} 2
=> δ
L = { Ok!, Err-a!, Err-P!} U 3
=> δ
June, 2005

25. Saturation
June, 2005

26. γ δ δ δ amount! card! card! card? γ δ γ δ δ γ card! Pin? Err-P! γ δ δ
γ δ δ δ
amount!
card!
card!
card?
x > 5
x := 0 γ δ 2 1 3 γ δ 2 3 1 δ 2 3 γ 1
card!
x > 5
Pin?
x ≤ 5
Err-P!
x := 0
γ δ δ
card!
x  5
Err-a! τ τ
x ≤ 5
x ≤ 5
Ok!
x := 0 γ δ 2 3 1
γ δ δ
γ δ δ δ 2 3 γ 1 δ
amount?
x ≤ 5
Ok!
x := 0 γ δ 2 1
x  5 τ τ
x ≤ 5
x ≤ 5
γ γ δ δ
γ γ δ δ
June, 2005

27. Ttraces ε(2).δ.ε(4).a?.γ.ε(3).b!.ε(2).c?.ε(1).a?.ε(3).b!
M = 2 1
ε(6).δ.a?.γ.ε(3).b!.ε(2).c?.ε(1).a?.ε(3).b! 1 3
ε(2).δ.ε(4).a?.γ.ε(3).b!.ε(2).c?.ε(1).a?.ε(3).b! 1 3
δ(2).a?(4).γ (0).b!(3).c?(2).a?(1).b!(3) 3 1
ε(6).a?.ε(3).b!.ε(2).c?.ε(1).a?.ε(3).b!
June, 2005

28. δ (2).c?(4).γ (0).P?(3).Ok?(2).a?(1).E!(3)
card?
Ok!
Pin?
Err-P!
card!
Err-a!
amount!
x5
x := 0
x ≤ 5 τ
amount?
γ δ δ δ
γ δ δ
γ γ δ δ γ δ 2 1 3
x > 5
δ (2).c?(4).γ (0).P?(3).Ok?(2).a?(1).E!(3) 1
June, 2005

29. outM (s) = U outM (s) U U outM (s)
Outputs
outM (s) = U outM (s) U U outM (s)
outM (s) = { o!(d) | s => }
U { δ (M ) | j-quiescent(s =>)}
outM (s) = U { γ (d) | i-refusal(s =>)} o r
sS
sS o
o!(d)
ε(Mj) j j r
ε(d) i
June, 2005

30. card! Є outM (s after card?(2).δ (1).Pin?(2).Err-P!(3))
M = <M1, M2, M3> M1= 1 M2= 1 M3= 2
card! Є outM (s after card?(2).δ (1).Pin?(2).Err-P!(3))
outM (s after σ) = ∅  σ Є nttraces(s) 1
June, 2005

31. Timed multi input-output implementation relation
mtiocoM
impl mtioco spec iff
 : outM (impl after  )  outM (spec after  ) M
ΔM(spec)
June, 2005

32. Test mtiocoM-sound = conforming implementation not rejected
mtiocoM-complete
= non-conforming implementations can
be rejected
Apply recursively & non-deterministically ( initially S = {s0} )
1 end test case
PASS
allowed oj! after d time-units
choose k Є [0, max{M1,..,Mm}) and input μ Є LI
FAIL
forbidden oi! after d’ time-units
o1!
x=dn
x=d1
x=d’n’
x=k
x  k
tγi t1 tn
x:=0
x=d’1
on’! μ?
on! tμ
γ i
x=Mu δu
allowed oj! after d time-units
3 wait for output in channel j
FAIL
forbidden oi! after d’ time-units 
x=d’1
x=dn
x=d1
x=d’n’
x=Mu
xMj
tδj t1 tn
x:=0
o1!
on’!
on! j u
x=Mj
June, 2005

33. Future work
June, 2005

34. Confirm completeness (in the old sense)
Evaluate applicability in practical situations
Deal with the imprecision in measuring physical time
Integrate with data testing
June, 2005