# A Tentative Approach for the Wadge-Wagner Hierarchy of Regular Tree Languages of Index [0, 2]

@inproceedings{Duparc2015ATA, title={A Tentative Approach for the Wadge-Wagner Hierarchy of Regular Tree Languages of Index [0, 2]}, author={Jacques Duparc and Kevin Fournier}, booktitle={DCFS}, year={2015} }

We provide a hierarchy of tree languages recognised by nondeterministic parity tree automata with priorities in \(\{0,1,2\}\), whose length exceeds the first fixed point of the \(\varepsilon \) operation (that itself enumerates the fixed points of \(x\mapsto \omega ^x\)). We conjecture that, up to Wadge equivalence, it exhibits all regular tree languages of index \([0,2]\).

## One Citation

### of the Workshop Workshop on Trends in Tree Automata and Tree Transducers

- Computer Science, Mathematics
- 2016

An algorithm for computing the N best roots of a weighted hypergraph is proposed, in which the weight function is given over an idempotent and multiplicatively monotone semiring, and it is proved that the proposed algorithm is correct.

## References

SHOWING 1-10 OF 13 REFERENCES

### The Wadge Hierarchy of Deterministic Tree Languages

- Computer ScienceLog. Methods Comput. Sci.
- 2006

An elementary procedure to decide if one deterministic tree language is continuously reducible to another is given, which extends Wagner's results on the hierarchy of omega-regular languages of words to the case of trees.

### On the Topological Complexity of Weakly Recognizable Tree Languages

- Computer ScienceFCT
- 2007

We show that the family of tree languages recognized by weak alternating automata is closed by three set theoretic operations that correspond to sum, multiplication by ordinals < ωω, and…

### On the topological complexity of tree languages

- Computer ScienceLogic and Automata
- 2008

The article surveys recent results in the study of topological complexity of recognizable tree languages. Emphasis is put on the relation between topological hierarchies, like the Borel hierarchy or…

### On Recognizable Tree Languages Beyond the Borel Hierarchy

- Computer ScienceFundam. Informaticae
- 2009

The topological complexity of non Borel recognizable tree languages with regard to the difference hierarchy of analytic sets is investigated and it is proved that the D$_{ω^n}$(Σ$^1_1$)-complete tree languages L$_n$ are Wadge reducible to the game tree language W$(i,κ)}$ for κ−ig 2.

### MSO on the Infinite Binary Tree: Choice and Order

- Computer ScienceCSL
- 2007

It is shown that every infinite binary tree with a well-founded order has an undecidable MSO-theory, and some applications of the result concerning unambiguous tree automata and definability of winning strategies in infinite games are discussed.

### Choice functions and well-orderings over the infinite binary tree

- Computer Science, Mathematics
- 2010

A new proof is given showing that it is not possible to define in monadic second-order logic (MSO) a choice function on the infinite binary tree and how the result can be used to prove the inherent ambiguity of languages of infinite trees.

### Decidability of second-order theories and automata on infinite trees

- Mathematics
- 1968

Introduction. In this paper we solve the decision problem of a certain secondorder mathematical theory and apply it to obtain a large number of decidability results. The method of solution involves…

### Wadge hierarchy and Veblen hierarchy Part I: Borel sets of finite rank

- MathematicsJournal of Symbolic Logic
- 2001

A “normal form” of A is obtained, by finding a Borel set Ω, such that A and Ω continuously reduce to each other, under the map which sends every Borel sets A of finite rank to its Wadge degree.