Elementary net systems (ENS) are the most fundamental class of Petri nets. Given a labeled transition system (TS) A, feasibility is the NP-complete decision problem whether A can be synthesized into an ENS. We analyze the impact of state degree, the number of allowed successors and predecessors of states in A, and event manifoldness, the amount of occurrences that an event can have in A, on the computational complexity of feasibility and the related event state separation property (ESSP) and state separation property (SSP). Feasibility, ESSP and SSP are NP-complete for TSs with state degree one and event manifoldness not less than three and for TSs with state degree and event manifoldness at least two. As we also show that SSP becomes tractable for TSs with state degree one and event manifoldness two, the only cases left open are ESSP and feasibility for the same input restriction.

基本网系统（ENS）是Petri网的最基本类别。给定带标签的过渡系统（TS）A，可行性是NP完全决策问题，即是否可以将A合成为ENS。我们分析状态程度的影响，在允许的继承人和美国的前辈数一，和事件manifoldness，发生一个事件可以在量一关于可行性的计算复杂性以及相关的事件状态分离属性（ESSP）和状态分离属性（SSP）。对于状态等级为1和事件流形不小于3的TS，对于状态等级和事件流形为至少2的TS，可行性，ESSP和SSP都是NP完全的。正如我们还表明的那样，对于状态状态为1和事件流形为2的TS，SSP变得易于处理，唯一剩下的情况是ESSP和相同输入限制的可行性。