Theorie reaktiver Systeme Requirement Coverage Tests Robustness Tests Test ¨Aquivalenz

Theorie reaktiver Systeme

Requirement Coverage Tests Robustness Tests

Test ¨Aquivalenz

Wiederholung

Safety Tests: Menge von Tests, die entscheidet, ob ^traces(^Q) ⊆ ^traces(^P).

U_S(^s, ^a) = if ^s = h i

then ω → STOP ₂ ^a → STOP

else ω → STOP ₂ ^head(^s) → ^U_S(^tail(^s), ^a)

H_Trace(^P) = {^U_S(^s, ^a) | ^s ∈ ^traces(^P) ∧ ^a ∈ α(^P) ∧ ^a 6∈ ^first(^P/^s)}.

Falls ^{Q must U}_S(^s, ^a) f¨ur alle ^U_S(^s, ^a) ∈ H_Trace(^P),

Requirement Coverage Tests

Gegeben ist ^P in Head-Normal-Form,

P = Q

i∈^I(₂ ^a : ^B_i.^a → ^Q_i(^a))

A ist minimale Coverage-Testmenge der L¨ange 1 f¨ur ^P: U_A = (₂ ^a ∈ ^A.^a → ω → STOP)

mit ^A = {^a₁, . . . , ^a_l} mit

∀ ⁱ ∈ ^I : {^a₁, . . . , ^a_l} ∩ ^B_i 6= ∅

∧ ∀ ^j ∈ {1, . . . , ^l}. ∃ ⁱ ∈ ^I.({^a₁, . . . , ^a_l} − {^a_j}) ∩ ^B_i = ∅

Requirement Coverage Tests

U_C(^s, ^A) = if ^s = h i

then ₂ ^a : ^A.^a → ω → STOP

else ω → STOP ₂ ^head(^s) → ^U_C(^tail(^s), ^A)

f¨ur ^s ∈ ^traces(^P) und ^A minimale Coverage Testmenge der L¨ange 1 f¨ur ^P/^s.

Requirement Coverage Tests

H_Req(^P) = {^U_C(^s, ^A) | ^s ∈ ^traces(^P) ∧

A minimale Coverage-Testmenge der L¨ange 1 f¨ur ^P/^s}.

P must U_C(^s, ^A) f¨ur alle ^U_C(^s, ^A) ∈ H_Req(^P).

H_Req(^P) ist minimal.

Robustness Tests

U_R(^s) = if ^s = h i

then ω → STOP

else ^head(^s) → ^U_R(^tail(^s))

H_Robust(^P) = {^U_R(^s) | ^s ∈ ^traces(^P) ∧ ∀ ^u ∈ ^traces(^P) : s ≤ ^u ∧ ^first(^P/^u) = ∅ → ^s = ^u}.

Testing ¨Aquivalenz

P ∼_TE ^Q ⇔

1. ^P must ^U_S(^s, ^a) ⇒ ^Q must ^U_S(^s, ^a)

2. ^P may ^U_R(^s) ⇒ ^Q may ^U_R(^s)

3. ^P must ^U_C(^s, ^A) ⇔ ^Q must ^U_C(^s, ^A)