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Wadge Degrees of -Languages of Petri Nets
Abstract
We prove that -languages of (non-deterministic) Petri nets and -languages of (non-deterministic) Turing machines have the same topological complexity: the Borel and Wadge hierarchies of the class of -languages of (non-deterministic) Petri nets are equal to the Borel and Wadge hierarchies of the class of -languages of (non-deterministic) Turing machines which also form the class of effective analytic sets. In particular, for each non-null recursive ordinal there exist some -complete and some -complete -languages of Petri nets, and the supremum of the set of Borel ranks of -languages of Petri nets is the ordinal , which is strictly greater than the first non-recursive ordinal . We also prove that there are some -complete, hence non-Borel, -languages of Petri nets, and that it is consistent with ZFC that there exist some -languages of Petri nets which are neither Borel nor -complete. This answers the question of the topological complexity of -languages of (non-deterministic) Petri nets which was left open in [DFR14,FS14]- info:eu-repo/semantics/preprint
- Preprints, Working Papers, ...
- Borel hierarchy
- Wadge hierarchy
- Wadge degrees
- infinite words
- Petri nets
- Cantor topology
- logic in computer science
- Automata and formal languages
- [INFO.INFO-LO]Computer Science [cs]/Logic in Computer Science [cs.LO]
- [MATH.MATH-LO]Mathematics [math]/Logic [math.LO]
- [INFO.INFO-GT]Computer Science [cs]/Computer Science and Game Theory [cs.GT]