The Emptiness Problem for Valence Automata or: Another Decidable Extension of Petri Nets
This work studies which storage mechanisms in automata permit decidability of the reachability problem. The question is formalized using valence automata, an abstract model that generalizes automata with storage. For each of a variety of storage mechanisms, one can choose a (typically infinite) monoid M such that valence automata over M are equivalent to (one-way) automata with this type of storage.
In fact, many interesting storage mechanisms can be realized by monoids defined by finite graphs, called graph monoids. Hence, we study for which graph monoids the emptiness problem for valence automata is decidable. A particular model realized by graph monoids is that of Petri nets with a pushdown stack. For these, decidability is a long-standing open question and we do not answer it here.
However, if one excludes subgraphs corresponding to this model, a characterization can be achieved. This characterization yields a new extension of Petri nets with a decidable reachability problem. Moreover, we provide a description of those storage mechanisms for which decidability remains open. This leads to a natural model that generalizes both pushdown Petri nets and priority multicounter machines.
KeywordsFree Product Storage Mechanism Reachability Problem Counter Machine Looped Vertex
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