Table 1 Parameter and explanation of the DA-NET model

a _i

Elements of the transition node set, a_i ∈ A, a_i = (Dⁱ, Fⁱ)

A

Transition node set, A = {a₁, a₂, ⋯}

\( {c}_k^i \)

Elements of the place node attribute set

C ⁱ

Attribute set of the place node, \( {C}^i=\left\{{c}_i^1,{c}_i^2,\cdots \right\} \)

\( {d}_k^j \)

Elements of the transition node attribute set

D ^j

Attribute set of the transition node, \( {D}^i=\left\{{d}_j^1,{d}_j^2,\cdots \right\} \)

\( {f}_k^j \)

Elements of the transition node algorithm set

F ^j

Algorithm set transition node, \( {F}^j=\left\{{f}_j^1,{f}_j^2,\cdots \right\} \)

E ^j

Decision logic of the transition node

G

Incidence matrix, where algorithm set G = O − I

\( {h}_k^i \)

Elements of the transition firing vector, \( {h}_k^i\in {H}^i \)

H ⁱ

Transition fire vector, \( {H}^i=\left[{h}_1^i,{h}_2^i,\cdots \right] \)

l _i

Elements of the arc set

I

Input matrix mapping, A × M → {0, 1}

L

Set of arcs, L = {l₁, l₂⋯}, L ⊆ M × A

O

Output matrix mapping, A × M → {0, 1}

m _i

Elements of the place node set, m_i ∈ M

M

Place node set M = {m₁, m₂, ⋯}

p _i

Elements of the node set, p_i ∈ P

P

Set of nodes, P = {p₁, p₂, ⋯}, P = M ∪ A

R(Tⁱ)

Reachable set of DA-NET markings from Tⁱ

\( {t}_j^i \)

Number of tokens of the place node in marking Tⁱ

T ⁱ

Marking of DA-NET, \( {T}^i=\left\{{t}_1^i,{t}_2^i,\cdots \right\} \)