xoEPC - Jan Mendling

3.4. EPC Semantics 87
is set to dead and the output context to wait. (2) For XOR-connectors, one input token
is consumed from one input arc and propagated to one of the output arcs if all of them
are empty. The respective input arc is set to a dead context, as well as those output arcs
that do not receive the token. The output arc with the positive token gets a wait context.
(3) For OR-splits, the positive token is consumed from the input, and a combination of
positive and negative tokens is produced at the output arcs such that at least one positive
token is available. Furthermore, each output arc with a positive token gets a wait context
while the others get a dead context. (4) OR-joins fire either if all input arcs are not empty
and one of them has a positive token, or if there is no empty arc with a wait context
and at least one positive token on the inputs. Then, all input tokens are consumed, plus
potentially negative tokens on the negative upper corona, the input arcs are set to a dead
context, and a positive token is produced on the output with a wait context.
Definition 3.20 (Transition Relation for Positive State Propagation). Let EP C =
(E, F, C, l, A) be a relaxed syntactically correct EPC, N = E ∪ F ∪ C its set of nodes,
and MEP C its marking space. Then R +1 ⊆ MEP C × N × MEP C is the transition relation
for positive state propagation and (m, n, m ′ ) ∈ R +1 if and only if:
((n ∈ F ∪ Eint ∪ Cand) ∧
(∀a∈nin : σm(a) = +1) ∧
(∀a∈nout : σm(a) = 0) ∧
(∀a∈nin
: σm ′(a) = 0 ∧ κm ′(a) = dead) ∧
(∀a∈nout : σm ′(a) = +1 ∧ κm ′(a) = wait) ∧
(∀a∈A\(nin∪nout) : κm ′(a) = κm(a)) ∧
(∀a∈A\(nin∪nout) : σm ′(a) = σm(a)))
∨
((n ∈ Cxor) ∧
(∃a1∈nin : (σm(a1) = +1 ∧ σm ′(a1) = 0 ∧
κm(a1) = wait ∧ κm ′(a1) = dead) ∧
(∀a∈nout : σm(a) = 0) ∧
(∃X∧a2∈nout : X = {a ∈ nin | σm(a) = −1 ∧ κm(a) = dead} ∧
(σm ′(a2) = +1 ∧ κm ′(a2) = wait) ∧
(∀a∈A\{a1,a2} : κm ′(a) = κm(a)) ∧