Confusion Analysis and Detection for Workflow Nets

Algorithm 1

Detection of confusion subnets in WF-net 𝑁.

(1)  Input: WF-net 𝑁=(𝑃,𝑇,𝐹).

(2)  Output: The set 𝑄_ci of CIC subnets and the set 𝑄_cd of CDC subnets.

(3)  𝑄_ci∶=∅, 𝑄_cd∶=∅, ℎ∶=0.

(4)  for each 𝑡_𝑖,𝑡_𝑗,𝑡_𝑘∈𝑇, 𝑖≠𝑗≠𝑘  do

(5)  if  ^•𝑡_𝑖∪𝑡^•_𝑖∩^•𝑡_𝑗∪𝑡^•_𝑗=∅∧𝑡_𝑘∈𝑡^•_𝑗^•∧^•𝑡_𝑖∩^•𝑡_𝑘≠∅  then

(6)   Capture a CIC subnet 𝑁_ℎ=𝑃_ℎ,𝑇_ℎ,𝐹_ℎ, where

   (1)  𝑃_ℎ∶=^•𝑇𝐾,𝑡_𝑘∪𝑇𝐾,𝑡_𝑘^•∪^•𝑡_𝑗∪𝑡^•_𝑗∩^•𝑇𝐾,𝑡_𝑘,

   (2)  𝑇_ℎ∶=𝑇𝐾,𝑡_𝑘∪𝑡_𝑗, and

   (3)  𝐹_ℎ∶=𝐹∩𝑃_ℎ×𝑇_ℎ∪𝑇_ℎ×𝑃_ℎ.

(7)   if  𝑁_ℎ∉𝑄_ci  then

(8)     ℎ∶=ℎ+1, 𝑄_ci∶=𝑄_ci∪𝑁_ℎ.

(9)   else

(10)     𝑄_ci∶=𝑄_ci.

(11)   end if

(12)  end if

(13)  end for

(14)  for each 𝑡_𝑖,𝑡_𝑗∈𝑇, 𝑖≠𝑗  do

(15)  If   ^•𝑡_𝑖∪𝑡^•_𝑖∩^•𝑡_𝑗∪𝑡^•_𝑗=∅∧^•𝑡_𝑖^•∩^•𝑡_𝑗^•≠∅

   then

(16)   Capture a CDC subnet 𝑁_ℎ=𝑃_ℎ,𝑇_ℎ,𝐹_ℎ, where

   (1)   𝑃_ℎ∶=^•𝑇𝐾,𝑡_𝑖∪𝑇𝐾,𝑡_𝑖^•∪^•𝑇𝐾,𝑡_𝑗∪𝑇𝐾,𝑡_𝑗^•,

   (2)   𝑇_ℎ∶=𝑇𝐾,𝑡_𝑖∪𝑇𝐾,𝑡_𝑗, and

   (3)   𝐹_ℎ∶=𝐹∩𝑃_ℎ×𝑇_ℎ∪𝑇_ℎ×𝑃_ℎ.

(17)   if  𝑁_ℎ∉𝑄_cd  then

(18)     ℎ∶=ℎ+1, 𝑄_cd∶=𝑄_cd∪𝑁_ℎ.

(19)   else

(20)     𝑄_cd∶=𝑄_cd.

(21)   end if

(22)  end if

(23)  end for

(24)  Output: 𝑄_ci and 𝑄_cd.