P-time event graphs are discrete event systems able to model cyclic production systems where tasks need to be performed within given time windows. Consistency is the property of admitting an infinite execution of such tasks that does not violate any temporal constraints. In this paper, we solve the long-standing problem of characterizing the decidability of consistency by showing that, assuming unary encoding of the initial marking, this property can be verified in strongly polynomial time. The proof is based on a reduction to the problem of detecting paths with infinite weight in infinite weighted digraphs called N-periodic graphs.

翻译：P时间事件图是离散事件系统，能够对需要在给定时间窗口内执行任务的循环生产系统进行建模。一致性是指系统允许无限执行这些任务且不违反任何时间约束的性质。本文解决了长期悬而未决的一致性可判定性刻画问题，证明在初始标识采用一元编码的假设下，该性质可在强多项式时间内得到验证。证明基于将问题归约为检测称为N周期图的无限加权有向图中具有无限权重的路径。