xoEPC - Jan Mendling

88 3. Event-driven Process Chains (EPC)
∨
((n ∈ Sor) ∧
(∀a∈X : σm ′(a) = 0 ∧ κm ′(a) = κm(a)) ∧
(∀a∈A\(X∪{a1,a2}) : σm ′(a) = σm(a)))))
(∀a∈nin : σm(a) = +1) ∧
(∀a∈nout : σm(a) = 0) ∧
(∀a∈nin
: σm ′(a) = 0 ∧ κm ′(a) = dead) ∧
(∃X�=∅ : X = {a ∈ nout | σm ′(a) = +1 ∧ κm ′(a) = wait} ∧
(∀a∈nout\X : σm ′(a) = −1 ∧ κm ′(a) = dead) ∧
(∀a∈A\(nin∪nout) : κm ′(a) = κm(a) ∧ σm ′(a) = σm(a)))
∨
((n ∈ Jor) ∧
(∃X�=∅ : X = {a ∈ nin | σm(a) = +1 ∧ κm(a) = wait}) ∧
(∃Y : Y = {a ∈ nin | σm(a) = −1 ∧ κm(a) = dead}) ∧
(∃Z : Z = {a ∈ nin | σm(a) = 0 ∧ κm(a) = dead}) ∧
(X ∪ Y ∪ Z = nin) ∧
(∀a∈nout : σm(a) = 0) ∧
(∀a∈nin
: σm ′(a) = 0 ∧ κm ′(a) = dead)) ∧
(∀a∈nout : σm ′(a) = +1 ∧ κm ′(a) = wait) ∧
(∃U⊂A : U = −1
↩→n ∧
m
(∀a∈U : σm ′(a) = 0 ∧ κm ′(a) = κm(a)) ∧
(∀a∈A\(U∪nin∪nout) : σm ′(a) = σm(a) ∧ κm ′(a) = κm(a)))).
Furthermore, we define the following notations:
• m1
n
→ +1 m2 if and only if (m1, n, m2) ∈ R +1 . We say that in the positive state
propagation phase marking m1 enables node n and its firing results in m2.
• m → m
+1 ′ n
if and only if ∃n : m1 → m2.
+1
• m τ → +1 m ′ if and only if ∃n1,...,nq,m1,...,mq+1 : τ = n1n2...nq ∈ N ∗ ∧
m1 = m ∧ mq+1 = m ′ ∧ m1
n1
→ m2, m2
+1
n2
→ ...
+1 nq
→ mq+1.
+1