Abstract
We prove that omega -languages of (non-deterministic) Petri nets and omega -languages of (non-deterministic) Turing machines have the same topological complexity: the Borel and Wadge hierarchies of the class of omega -languages of (non-deterministic) Petri nets are equal to the Borel and Wadge hierarchies of the class of omega -languages of (non-deterministic) Turing machines. We also show that it is highly undecidable to determine the topological complexity of a Petri net omega -language. Moreover, we infer from the proofs of the above results that the equivalence and the inclusion problems for omega -languages of Petri nets are varPi _2^1-complete, hence also highly undecidable.
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