基于Petri网局部性的极大冲突集枚举算法

冲突是Petri网研究的重要主题.目前Petri网冲突研究主要集中于冲突建模和冲突消解策略，而对冲突问题本身的计算复杂性却很少关注.提出Petri网的冲突集问题，并证明冲突集问题是NP（Non-deterministic Polynomial）完全的.提出极大冲突集动态枚举算法，该算法基于当前标识的所有极大冲突集，利用Petri网实施局部性，仅计算下一标识中受局部性影响的极大冲突集，从而避免重新枚举所有极大冲突集.该算法时间复杂度为O（m²n），m是当前标识的极大冲突集数目，n是变迁数.最后证明自由选择网、非对称选择网的极大冲突集枚举算法复杂度可降至O（n²）.极大冲突集枚举算法研究将为Petri网冲突问题的算法求解提供理论参考.

Maximal Conflict Set Enumeration Algorithm Based on Locality of Petri Nets

Conflict is an essential concept in Petri net theory.The existing research focuses on the modelling and resolu-tion strategies of conflict problems,but less on the computational complexity of the problems theirselves.In this paper,we pro-pose the conflict set problem for Petri nets,and prove that the conflict set problem is NP-complete.Furthermore,we present a dynamic algorithm for the maximal conflict set enumeration.Our algorithm only computes those conflict sets that are affected by local firing,which avoids enumerating all maximal conflict sets at each marking.The algorithm needs time O(m2n)where m is the number of maximal conflict sets at the current marking and n is the number of transitions.Finally,we show that the maximal conflict set enumeration problem can be solved in O(n2)for free-choice nets and asymmetric choice nets.The results on complexity of thel conflict set problem provide a theoretical reference for solving conflict problems of Petri nets.