Corpus ID: 29209552

# Wadge Degrees of ω-Languages of Petri Nets

@article{Finkel2017WadgeDO,
title={Wadge Degrees of $\omega$-Languages of Petri Nets},
author={O. Finkel},
journal={ArXiv},
year={2017},
volume={abs/1712.07945}
}
• O. Finkel
• Published 2017
• Computer Science, Mathematics
• ArXiv
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 which also form the class of effective analytic sets. In particular, for each non-null recursive ordinal α < ωCK 1 there exist some Σ 0… Expand
3 Citations

#### Topics from this paper

On the expressive power of non-deterministic and unambiguous Petri nets over infinite words
• Computer Science
• ArXiv
• 2021
It is shown that it is highly undecidable to determine the topological complexity of a Petri net ω-language, and it is entail that the υ-languages recognisable by unambiguous Petri nets are ∆03 sets. Expand
On the High Complexity of Petri Nets -Languages
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 classExpand
Application and Theory of Petri Nets and Concurrency: 41st International Conference, PETRI NETS 2020, Paris, France, June 24–25, 2020, Proceedings
• Computer Science
• Petri Nets
• 2020
This article reformulates this problem as the transformation of an ordinary, one-safe Petri net into a flat, unit-safe NUPN (Nested-Unit Petri Net) and defines a quality criterion based on the number of bits required for the structural encoding of markings. Expand

#### References

SHOWING 1-10 OF 44 REFERENCES
Topological properties of omega context-free languages
• O. Finkel
• Computer Science, Mathematics
• Theor. Comput. Sci.
• 2001
It is shown that Buchi–Landweber's Theorem cannot be extended to even closed ω - CFL : in a Gale–Stewart game with a (closed) ω- CFL winning set, one cannot decide which player has a winning strategy. Expand
Wadge Degrees of Infinitary Rational Relations
• O. Finkel
• Computer Science, Mathematics
• Math. Comput. Sci.
• 2008
The Borel and the Wadge hierarchies of the class RATω of infinitary rational relations accepted by 2-tape Büchi automata are equal to the Borel-Wadge hierarchy of ω-languages accepted by real-time BüCHI 1-counter automata or by B Müchi Turing machines. Expand
The determinacy of context-free games
• O. Finkel
• Mathematics, Computer Science
• J. Symb. Log.
• 2013
We prove that the determinacy of Gale-Stewart games whose winning sets are accepted by real-time 1-counter Buchi automata is equivalent to the determinacy of (effective) analytic Gale-Stewart gamesExpand
The Wadge Hierarchy of Petri Nets ω-Languages
• Mathematics, Computer Science
• LFCS
• 2013
The Wadge hierarchy of the ω-languages recognized by deterministic Petri nets is described, and it is shown that the whole hierarchy has height $$\omega^{\omega^{2}$$, and the restrictions of this hierarchy to every fixed number of partially blind counters are given. Expand
Borel hierarchy and omega context free languages
• O. Finkel
• Computer Science, Mathematics
• Theor. Comput. Sci.
• 2003
This paper proves topological properties of omega context free languages (�-CFL) which extend those of O. Finkel (Theoret. Expand
Decision problems forω-automata
• L. Landweber
• Computer Science, Mathematics
• Mathematical systems theory
• 2005
This paper considers various definitions for machines of this type, including ones introduced by Biichi and McNaughton, and classify the complexity of definable sets of sequences for each type of finite automaton. Expand
Computer science and the fine structure of Borel sets
• Computer Science, Mathematics
• Theor. Comput. Sci.
• 2001
This work gives a transparent restatement and proof of Wadge's main theorem, and extends Wagner's results to more general kinds of automata: counters, push-down automata and Buchi automata reading transfinite words. Expand
On the topological complexity of ω-languages of non-deterministic Petri nets
• Mathematics, Computer Science
• Inf. Process. Lett.
• 2014
We show that there are @S"3^0-complete languages of infinite words accepted by non-deterministic Petri nets with Buchi acceptance condition, or equivalently by Buchi blind counter automata. ThisExpand
Wadge degrees of ω-languages of deterministic Turing machines
We describe Wadge degrees of ω-languages recognizable by deterministic Turing machines. In particular, it is shown that the ordinal corresponding to these degrees is ξ ω where ξ = ω CK 1 is the firstExpand
Logical Specifications of Infinite Computations
• Mathematics, Computer Science
• REX School/Symposium
• 1993
The automaton theoretic approach to logical specifications over ω-words turns out to be a technique to reduce quantifier complexity of formulas. Expand