Conflict is an essential concept in Petri net theory.The existing research focuses on the modelling and resolution strategies of conflict problems

but less on the computational complexity of the problems theirselves.In this paper

we propose 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.