# Degrees of Transducibility

@inproceedings{Endrullis2015DegreesOT, title={Degrees of Transducibility}, author={J{\"o}rg Endrullis and Jan Willem Klop and Aleksi Saarela and Markus A. Whiteland}, booktitle={Words}, year={2015} }

Our objects of study are infinite sequences and how they can be transformed into each other. As transformational devices, we focus here on Turing Machines, sequential finite state transducers and Mealy Machines. For each of these choices, the resulting transducibility relation \(\ge \) is a preorder on the set of infinite sequences. This preorder induces equivalence classes, called degrees, and a partial order on the degrees.

## 12 Citations

### Degrees of Infinite Words, Polynomials, and Atoms (Extended Version)

- Computer ScienceArXiv
- 2018

Finite-state transducers and their power for transforming infinite words are studied and methods from linear algebra and analysis are used to show that there are infinitely many atoms in the transducer degrees, that is, minimal non-trivial degrees.

### Degrees of Infinite Words, Polynomials and Atoms

- Computer ScienceDLT
- 2016

Finite-state transducers and their power for transforming infinite words are studied and methods from linear algebra and analysis are used to show that there are infinitely many atoms in the transducer degrees, that is, minimal non-trivial degrees.

### Classifying Non-periodic Sequences by Permutation Transducers

- MathematicsDLT
- 2017

This work investigates this hierarchy for non-periodic sequences over \(\{0,1\}\) in which the groups of 0s and 1s grow according to simple functions like polynomials, finding infinite strictly ascending chains of sequences, all being equivalent with respect to ordinary transducers.

### On the Complexity of Infinite Advice Strings

- Computer ScienceICALP
- 2018

The main results explore the connections between classes of advice automatic structures, MSO-transductions and two-way transducers and suggest a closer study of the resulting hierarchy over infinite words.

### Comparing the power of advice strings: a notion of complexity for infinite words

- Computer ScienceArXiv
- 2018

The main results explore the connections between classes of advice automatic structures, MSO-transductions and two-way transducers and suggest a closer study of the resulting hierarchy over infinite words.

### Notes on Decreasing Diagrams for Confluence and Commutation

- Computer Science
- 2019

This paper investigates the possibility of a confluence hierarchy, and determines the firstorder (non-definability) of the notion of confluence and related properties, using techniques from finite model theory.

### Decreasing Diagrams for Confluence and Commutation

- Computer ScienceLog. Methods Comput. Sci.
- 2020

This paper investigates the possibility of a confluence hierarchy, and determines the first-order (non-definability) of the notion of confluence and related properties, using techniques from finite model theory.

### Transducer degrees: atoms, infima and suprema

- PhysicsActa Informatica
- 2019

Although finite state transducers are very natural and simple devices, surprisingly little is known about the transducibility relation they induce on streams (infinite words). We collect some…

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