Confusion Analysis and Detection for Workflow Nets

Algorithm 2

Detection of confusions by the ILP in WF-system (𝑁,𝑀_in).

(1)  Input: WF-system 𝑁,𝑀_in, 𝑄_ci, and 𝑄_cd.

(2)  Output: The set 𝑄_ci of CICs and the set 𝑄_cd of CDCs.

(3)  𝑄_ci∶=∅, 𝑄_cd∶=∅,

(4)  for each 𝑁_ℎ∈𝑄_ci  do

(5)  Compute [𝑁]^𝑇⋅𝐼=𝟎 to obtain all minimal 𝑃-invariants 𝐼₁,𝐼₂,…, and 𝐼_𝑛.

(6)  Find 𝐾=𝑝,𝑇(𝐾) in 𝑁_ℎ.

(7)  Ω₁∶=𝑇⧵𝑇(𝐾), Ω₂∶=𝑇(𝐾)⧵𝑇(𝐾)∩Ω^•₁^•.

(8)  Compute the value 𝜐 of following ILP:

     maxΣ_{𝑝∈•(Ω1∪Ω2)}𝑀𝑝s.t.∶Σ_{𝑝∈||𝐼1||}𝑀𝑝=𝑀_in𝑝_inΣ=1_{𝑝∈||𝐼2||}𝑀𝑝=𝑀_in𝑝_in⋮Σ=1,_{𝑝∈||𝐼𝑛||}𝑀𝑝=𝑀_in𝑝_in=1.

(9)  if  𝜐=^•Ω₁∪Ω₂  then

(10)   𝑀∶=Σ_{𝑝∈•(Ω1∪Ω2)}𝑀𝑝𝑝.

(11)   𝑄_ci∶=𝑄_ci∪𝑁_ℎ,𝑀.

(12)  else

(13)  𝑄_ci∶=𝑄_ci.

(14)  end if

(15)  end for

(16)  for each 𝑁_ℎ∈𝑄_cd  do

(17)  Compute [𝑁]^𝑇⋅𝐼=𝟎 to obtain all minimal 𝑃-invariants 𝐼₁,𝐼₂,…, and 𝐼_𝑛.

(18)  Compute the value 𝜐 of following ILP:

     maxΣ_{𝑝∈•𝑇}𝑀𝑝s.t.∶Σ_{𝑝∈||𝐼1||}𝑀𝑝=𝑀_in𝑝_inΣ=1_{𝑝∈||𝐼2||}𝑀𝑝=𝑀_in𝑝_in⋮Σ=1,_{𝑝∈||𝐼𝑛||}𝑀𝑝=𝑀_in𝑝_in=1.

(19)  if  𝜐=^•𝑇  then

(20)   𝑀∶=Σ_{𝑝∈•𝑇}𝑀𝑝𝑝.

(21)   𝑄_cd∶=𝑄_cd∪𝑁_ℎ,𝑀.

(22)  else

(23)   𝑄_cd∶=𝑄_cd.

(24)  end if

(25)  end for

(26)  Output: 𝑄_ci and 𝑄_cd.