This document discusses symbolic test generation for compositional real-time systems. It motivates the research by explaining that real-time systems have both behavioral and time constraints, and that testing subsystems individually can reduce costs but integration testing poses challenges. The problem is defined as how to validate the behavior of compositional real-time systems using symbolic specifications. The research questions aim to define composition operators for symbolic models, determine challenges in inferring conformance based on composites, and generate integration tests from composed models. Preliminary results include defining sequential and parallel composition operators and applying them in a case study.

1. Symbolic Test Generation of
Compositional Real-Time Systems
Adriana Damasceno – adriana@copin.ufcg.edu.br
Wilkerson Andrade – wilkerson@computacao.ufcg.edu.br
Patricia Machado – patricia@computacao.ufcg.edu.br

2. 2
Motivation
• Real-time systems → behaviour + time;
• Software tests and Timed Automata (TA) reduce project budgets;
• Conformance relations compare implementations and
specifications;
• The compositionality of real-time systems lessen their complexity;

3. 3
Motivation
• Integration testing of real-time systems bring many issues:
- Most real-time systems are distributed;
- Their integration can inject errors in the whole system;
- Tests can be developed from the subsystems or from the
composed result;
- Conformance can be infered from the isolated subsystems or
the composed specification.
C1
C1 C3
C3C2
C2
C6
C6 C7
C7

4. 4
Problem statement
tioco tioco
Implementation1
• tioco (timed input-output conformance)
Implementation3
S6
S7
S8
b?
x := 0
x < 4
a!
S13
S14
S15
b?
x := 0
x == 6
a!
d!
S0
S1
S2
Specification1
b?
x := 0
x < 5
a!

5. 5
Problem statement
tioco
Specification2
Implementation2
S3
S4
S5
c?
y := 0
y > 5
a?
a!
S10
S11
S12
a!
c?
y := 0
y > 7
a?

6. 6
Problem statement
Specification1 Specification2
Specification1
|| Specification2
S0
S1
S2
b?
x := 0
x < 5
a!
S3
S4
S5
c?
y := 0
y > 5
a?
a!
S0, S3
c?
y := 0
S1, S3 S0, S4
S1, S4
S2, S5
b?
x := 0
x < 5 AND y > 5
a!
b?
x := 0
c?
y := 0

7. 7
Problem statement
Implementation1
Implementation2
Implementation1
|| Implementation2
S6
S7
S8
b?
x := 0
x < 4
a!
S9
a?
S10
S11
S12
a!
c?
y := 0
y > 7
a?
S6, S10
S7, S10 S6, S11
S7, S11
x < 4 AND y > 7
a!
S8, S12
a!
S9, S12
b?
x := 0
b?
x := 0
c?
y := 0
c?
y := 0

8. 8
Problem statement
tioco
x > y
S0, S3
c?
y := 0
S1, S3 S0, S4
S1, S4
S2, S5
b?
x := 0
x < 5 AND y > 5
a!
Specification1
|| Specification2
b?
x := 0
c?
y := 0
S6, S10
S7, S10 S6, S11
S7, S11
x < 4 AND y > 7
a!
Implementation1
|| Implementation2
S8, S12
a!
S9, S12
b?
x := 0
b?
x := 0
c?
y := 0
c?
y := 0

9. 9
Problem statement
How to validate the behaviour of
compositional real-time systems using
symbolic specifications?

10. 10
Research questions
1)How symbolic models of real-time systems that
abstract data and time can be composed?
2)What are the main challenges to infer conformance of
the composed system based on conformance of
composites?
3)How can integration test cases be generated from
composed models?

11. 11
Expected contributions
• Define the parallel, sequential, renaming and hiding
operators;
• Present and prove properties about these operators;
• Propose a testing strategy that uses these operators;
• Identify dificulties in the test generation strategy;
• Implement the operators in a tool and validate the
results.

12. 12
Background
• Input-complete compositional timed automata
S0
S1
S2
S3
S4
S5
Specification1
b?
x := 0
x < 5
a!
c?
y := 0
y > 5
a?
Specification2
a!
LC2LC1
b?
a?
c?
c?, a?
y <= 5
a?
b?

13. 13
Background
• Input-complete Compositional Timed Automata
S6
S7
S8
b?
x := 0
x < 4
a!
Implementation1
Implementation2
LC3
a?, b?
S9
a?
a?
b?
a?, b?
S10
S11
S12
a!
c?
y := 0
y > 7
a?
LC4
a?
c?
c?, a?
y <= 7
a?

14. 14
Background
• Input-complete Compositional Timed Automata
• Resultado da composicionalidade

15. 15
Background
• TIOSTS

16. 16
Background
• Test case generation process

17. 17
Preliminary results
• Sequential operator
S0 S1 S2 S3 S4 S5
[var1
= p1
]
a!p1
G2
a?p1
{var2
:= p1
}
G01 G02
S0 S2,S4
var1
= p1
AND G02
AND G2
a!p1
{var2
:= p1
}
G01
S5
c?
b? c?
b?
S1,S3
T1
; T2
T1
T2

18. 18
Preliminary results
• Parallel operator
S3 S4 S5
G2
Gd
b?
Ge
a?
Gf
f!
S1 S2
Gb
b!
Ga
a!
Gc
c?
G1
G1
and G2
T1
T2
T1
|| T2
S1, S3 S2, S3 S1, S4 S2, S4 S1, S5
S2, S5
Gc
c?
Gd
and Gb
b!
Gc
c?
Ge
and Ga
a!
Gc
c?
S2, S5
Gf
f!
Gc
c?
Gf
f!

19. 19
Preliminary results
• Case study
Target
Designation
Target
Tracking
Radar
finishTargetDesignation
targetPosition
Tracking subsystem
6 locations and
7 transitions
11 locations and
12 transitions
9 locations and
9 transitions

20. 20
Preliminary results
• Case study
Target
Designation
Target
Tracking
Radar
finishTargetDesignation
targetPosition
Tracking subsystem
18 locations and
20 transitions

21. 21
Preliminary results
• Case study
Target
Designation
Target
Tracking
Radar
finishTargetDesignation
targetPosition
Tracking subsystem
72 locations and
143 transitions

22. 22
Reserach Activities
1) Define the sequential and parallel compositional operators;
2) Perform a case study on them and elaborate formal proofs;
3) Perform a systematic mapping;
4) Define and implement the renaming and hiding operators;
5) Perform case studies and elaborate formal proofs;
6) Give conclusions about the operators compositionality,
commutability and transitivity properties;
7) Write the thesis and an article with the remaining results.
Past
Future

23. 23
Final Remarks
• ???????

24. Symbolic Test Generation of
Compositional Real-Time Systems
Adriana Damasceno – adriana@copin.ufcg.edu.br
Wilkerson Andrade – wilkerson@computacao.ufcg.edu.br
Patricia Machado – patricia@computacao.ufcg.edu.br

25. 25
Systematic Mapping

26. 26
Preliminary Results
• Define the parallel, sequential, renaming and hiding
operators;
• Present and prove properties about these operators;
• Propose a testing strategy that uses these operators;
• Identify dificulties in the test generation strategy;
• Implement the operators in a tool and validate the
results.

27. 27
Systematic Mapping
• Define the parallel, sequential, renaming and hiding
operators;
• Present and prove properties about these operators;
• Propose a testing strategy that uses these operators;
• Identify dificulties in the test generation strategy;
• Implement the operators in a tool and validate the
results.

28. 28
Systematic Mapping
• Define the parallel, sequential, renaming and hiding
operators;
• Present and prove properties about these operators;
• Propose a testing strategy that uses these operators;
• Identify dificulties in the test generation strategy;
• Implement the operators in a tool and validate the
results.