On the High Complexity of Petri Nets $$\omega $$-Languages [chapter]

Olivier Finkel
2020 Lecture Notes in Computer Science  
We prove that ω-languages of (non-deterministic) Petri nets and ω-languages of (non-deterministic) Turing machines have the same topological complexity: the Borel and Wadge hierarchies of the class of ω-languages of (non-deterministic) Petri nets are equal to the Borel and Wadge hierarchies of the class of ω-languages of (non-deterministic) Turing machines. We also show that it is highly undecidable to determine the topological complexity of a Petri net ω-language. Moreover, we infer from the
more » ... oofs of the above results that the equivalence and the inclusion problems for ω-languages of Petri nets are Π 1 2 -complete, hence also highly undecidable.
doi:10.1007/978-3-030-51831-8_4 fatcat:3kxxriteq5ewropgozkc2vfnmu