On the High Complexity of Petri Nets $\omega$-Languages - Archive ouverte HAL
Conference Papers Year : 2020

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

Olivier Finkel
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Abstract

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 proofs 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.
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Dates and versions

hal-02898143 , version 1 (13-07-2020)

Identifiers

  • HAL Id : hal-02898143 , version 1

Cite

Olivier Finkel. On the High Complexity of Petri Nets $\omega$-Languages. 41st International Conference on Application and Theory of Petri Nets and Concurrency, PETRI NETS 2020, Jun 2020, Paris, France. pp.69-88. ⟨hal-02898143⟩
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