Lecture Notes in Computer Science 3472

210 Laura Brandán Briones and Mathias Röhl
Algorithm 11 Equivalence Class Graph
input: ERA determinized specification Spec
output: A equivalence Class Graph
1 S ′ 2
0 = {s0}
E = ∅ // E the set of transition
3 N = {[S ′ 0, p] | p ∈ Ψdnf (S ′ 4
0) ∧ p �= ∅} // N is the set of nodes
N ′ = N //N’isthesetofnewnodes
5 while N ′ �= ∅ then
6 N ′′′ = ∅
7 foreach [S ′ , p] ∈ N ′
8 foreach a ∈ Σ :
9 S ′′ = {s ′ |∃ s ∈ S ′ : s ϕ,a
−→ s ′ }
10 if S ′′ �= ∅ then
11 N ′′ = {[S ′′ , p ′ ] | p ′ ∈ Ψdnf (S ′′ ) ∧ p ′ 12
�= ∅}
E = E � {([S ′ , p], a, [S ′′ , p ′ ]) | [S ′′ , p ′ ] ∈ N ′′ 13
∧ (p ∧ ϕ) �= ∅}
N ′′′ = N ′′′ � N ′′
14 N ′ = N ′′′ − (N ′′′ � 15
N )
N = N � N ′
Definition 8.15. Decorated Equivalence Classes
Define Must([S ′ , p])={A | ∃〈S ′ , ν〉 : 〈S ′ , ν〉∈[S ′ , p] :〈S ′ , ν〉 |= after ɛ must A}
Sort([S ′ , p]) = {a | ∃ 〈S ′ , ν〉 : 〈S ′ , ν〉 ∈[S ′ , p] :〈S ′ , ν〉 a →}
• M ([S ′ , p]) = Must([S ′ , p])
• C ([S ′ , p]) = Sort([S ′ , p])
• R([S ′ , p]) = Σ − Sort([S ′ , p])
where ɛ denote the empty sequence.
If σ is a timed trace that lead to [S ′ , p] andA∈ M ([S ′ , p]) then: after σ
must A, is a test to be passed for that class. Similarly: after σ · a must ∅, isa
test to be passed if a ∈ R([S ′ , p]), and can σ · a if a ∈ C ([S ′ , p]). The number
of generated tests can be reduced by remove tests that are logically passed by
another test, i.e. the must sets can be reduced to M ([S ′ , p]) = min⊆Must([S ′ , p])
(where min⊆(M ) gives the set of minimal elements of M under subset inclusion),
and the actions observed during the execution of a must test can be removed
from the may tests, i.e. C ([S ′ , p]) = Sort([S ′ �
, p]) − A.
A∈M ([S ′ ,p])
Example. The equivalence classes graph for the automatic Light Switch are
shown in Figure 8.5.
The equivalence class graph preserves all timed traces of the specification, and
the required deadlock information for the Hennessy test [HN83] of the specification
by the M , C and R action sets is stored in each node. The non-determinism
found in the original specification is therefore maintained, but is represented differently,
in a way that is more convenient for test generation: a test is composed