The Petri net synthesis problem for automatic graphs

Automatic graphs are possibly infinite graphs with a rational presentation by finite automata; they include grids as a particular case, and Sénizergues has shown in a seminal work that they are an extension of deterministic pushdown graphs. Here, we propose a procedure that decides from the automatic presentation of a graph whether it may be realized isomorphically by the reachable state graph of some finite Petri net, with transitions in bijection with labels of edges. As automatic graphs cover more concurrent systems than pushdown graphs, this procedure improves over, and indeed subsumes, the net synthesis procedure studied earlier for pushdown graphs