We provide a counterexample to a conjecture by Thiagarajan (1996, 2002) that regular event structures correspond to event structures obtained as unfoldings of finite 1-safe Petri nets. The same counterexample is used to disprove a closely related conjecture by Badouel, Darondeau, and Raoult (1999). Using that domains of events structures are CAT(0) cube complexes, we construct our counterexample from an example by Wise (1996, 2007) of a nonpositively curved square complex whose universal cover contains an aperiodic plane. We prove that other counterexamples to Thiagarajan's conjecture arise from aperiodic 4-way deterministic tile sets of Kari and Papasoglu (1999) and Lukkarila (2009). On the positive side, using breakthrough results by Agol (2013) and Haglund and Wise (2008, 2012) from geometric group theory, we prove that Thiagarajan's conjecture holds for strongly hyperbolic regular event structures.

我们为Thiagarajan（1996，2002）的一个猜想提供了反例，即常规事件结构对应于作为有限1-安全Petri网的展开而获得的事件结构。Badouel，Darondeau和Raoult（1999）使用相同的反例来证明一个密切相关的猜想。利用事件结构的域是CAT（0）立方体复合物，我们从Wise（1996，2007）的例子中构造了一个反例，该例子是一个非正弯曲的正方形复合物，其通用覆盖层包含一个非周期性平面。我们证明，Thiagarajan猜想的其他反例来自Kari和Papasoglu（1999）和Lukkarila（2009）的非周期性4向确定性平铺集。从积极方面来看，利用几何群论的Agol（2013）和Haglund and Wise（2008，2012）的突破性结果，我们证明了Thiagarajan'