Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
124 tokens/sec
GPT-4o
8 tokens/sec
Gemini 2.5 Pro Pro
47 tokens/sec
o3 Pro
5 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Wadge Degrees of $ω$-Languages of Petri Nets (1712.07945v2)

Published 20 Dec 2017 in cs.LO and math.LO

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 which also form the class of effective analytic sets. In particular, for each non-null recursive ordinal $\alpha < \omega_1{{\rm CK}} $ there exist some ${\bf \Sigma}0_\alpha$-complete and some ${\bf \Pi}0_\alpha$-complete $\omega$-languages of Petri nets, and the supremum of the set of Borel ranks of $\omega$-languages of Petri nets is the ordinal $\gamma_21$, which is strictly greater than the first non-recursive ordinal $\omega_1{{\rm CK}}$. We also prove that there are some ${\bf \Sigma}_11$-complete, hence non-Borel, $\omega$-languages of Petri nets, and that it is consistent with ZFC that there exist some $\omega$-languages of Petri nets which are neither Borel nor ${\bf \Sigma}_11$-complete. This answers the question of the topological complexity of $\omega$-languages of (non-deterministic) Petri nets which was left open in [DFR14,FS14].

Citations (4)

Summary

We haven't generated a summary for this paper yet.