10、并发控制系统的SM分解方法详解

并发控制系统的SM分解方法详解

1. 基于图论的SM分解

• 算法6.1：通过NOPs补充组件
  • 输入 ：解释Petri网 $PN = (P, T, F, M_0, X, Y)$，$PN$ 的并发图 $GC = (P, ||A)$，$GC$ 着色过程中得到的集合 $S$。
  • 输出 ：若 $PN$ 分解正确，输出由 $NOPs$ 补充后的集合 $S$。

1: for all S = (P′, T ′, F′, M′0) ∈S do
2:     i = 1
3:     I ←∅
4:     O ←∅
5:     for all p ∈P′ do
6:         for each t ∈•p such that •t = ∅do I = I ∪{t}
7:         for each t ∈p• such that t• = ∅do O = O ∪{t}
8:     end for
9:     if [I ̸= ∅or O ̸= ∅] then
10:        if [I = ∅or O = ∅] then
11:            notify: “The net cannot be decomposed.”
12:            return
13:        else
14:            P′ = P′ ∪{N O Pi}
15:            for