# Unambiguous Tree Languages Are Topologically Harder Than Deterministic Ones

@inproceedings{Hummel2012UnambiguousTL, title={Unambiguous Tree Languages Are Topologically Harder Than Deterministic Ones}, author={Szczepan Hummel}, booktitle={GandALF}, year={2012} }

The paper gives an example of a tree language G that is recognised by an unambiguous parity automaton and is analytic-complete as a set in Cantor space. This already shows that the unambiguous languages are topologically more complex than the deterministic ones, that are all coanalytic.
Using set G as a building block we construct an unambiguous language that is topologically harder than any countable boolean combination of analytic and coanalytic sets. In particular the language is harderâ€¦Â

## 10 Citations

### Unambiguous languages exhaust the index hierarchy

- Computer ScienceICALP
- 2018

The question whether unambiguous languages are of bounded complexity among all regular tree languages is answered, as exhibited by a family of examples of unambiguity languages that cannot be recognised by any alternating parity tree automata of bounded range of priorities.

### Unambiguity and uniformization problems on infinite trees

- Computer ScienceCSL
- 2013

This work proposes a procedure P designed to decide if a given tree automaton recognizes a bi-unambiguous language, and conjecture that P is complete for all inputs but this depends on a new conjecture stating that there is no MSO-definable choice function on thin trees.

### On Unambiguous Regular Tree Languages of Index (0, 2)

- Computer ScienceCSL
- 2015

This work provides operations that generate a family (A_{alpha})_{alpha < phi_2(0)} of unambiguous automata such that it respects the strict Wadge ordering.

### Topological Complexity of Sets Defined by Automata and Formulas

- Computer Science
- 2017

By considering in nite structures a variety of complexity measures that come from descriptive set theory, the theory of de nability and the grammatical complexity of their definitions is measured.

### Introduction to Automaton Theory

- Computer Science

A game used to simulate the possible runs of a tree automaton will be introduced, which can prove Rabin's complementation theorem and the relations between logics and tree automata will be showed.

### An upper bound on the complexity of recognizable tree languages

- Computer ScienceRAIRO Theor. Informatics Appl.
- 2015

An embedding of the Wadge hierarchy of non self-dual Borel subsets of the Cantor space into the class of regular tree languages is argued to be much better than the usual ${\bf\Delta}^1\_2$.

### Unambiguous BÃ¼chi Is Weak

- Computer ScienceDLT
- 2016

The main theorem of this paper is a correctness proof of the transformation algorithm, which is based on a separation algorithm of Arnold and Santocanale 2005 and extends results of Finkel and Simonnet 2009.

### Descriptive Set Theoretic Methods in Automata Theory

- Computer ScienceLecture Notes in Computer Science
- 2016

Wyniki przedstawione w rozprawie sÄ… oparte o [HS12, FMS13, BIS13, BS13, Skr14, BGMS14] oraz raport techniczny [MS14], ktÃ³ra odnosi siÄ™ jedynie do automatÃ³w.

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