We present a transformation of the Dynamic Condition Response (DCR) graph constraint based process specification language to safe Petri Nets with inhibitor and read arcs, generalized with an acceptance criteria enabling the specification of the union of regular and ω -regular languages. We prove that the DCR graph and the resulting Petri Net are bisimilar and that the bisimulation respects the acceptance criterium. The transformation enables the capturing of regular and omega-regular process requirements from texts and event logs using existing tools for DCR requirements mapping and process mining. A representation of DCR Graphs as Petri Nets advances the understanding of the relationship between the two models and enables improved analysis and model checking capabilities for DCR graph specifications through mature Petri net tools. We provide a python script implementing the transformation from the DCR XML export format to the PNML exchange format extended with arc types. In the implementation, all read arcs are replaced by a pair of standard input and output arcs. This directly enables the simulation and analysis of the resulting Petri Nets in tools such as TAPAAL, but means that the acceptance criterium for infinite runs is not preserved.