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. 
View via Publisher
users.utu.fi
12 Citations
Background Citations
8
Methods Citations
2
Results Citations
2

12 Citations

Transducer degrees: atoms, infima and suprema

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…

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

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

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

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.

Ordering sequences by permutation transducers

On the Complexity of Infinite Advice Strings

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

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

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

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.

Braids via term rewriting

References

SHOWING 1-10 OF 20 REFERENCES

Some Algebraic Properties of Machine Poset of Infinite Words

The complexity of infinite words is considered from the point of view of a transformation with a Mealy machine that is the simplest model of a finite automaton transducer. We are mostly interested in…

Degrees of Streams

We introduce a novel approach to comparing the complexity of streams, namely in terms of reducibility by finite state transducers. This gives rise to a hierarchy of stream ‘degrees’, somewhat…

Degrees of Finite-State Transformability

  • G. Rayna
  • Mathematics, Computer Science
    Inf. Control.
  • 1974

The Upper Semi-Lattice of Degrees of Recursive Unsolvability

The concept 'degree of recursive unsolvability' was introduced briefly in Post [16]. In his abstract [17] the concept was formulated precisely via an extension of [15], and a resulting partial scale…

The Degree of Squares is an Atom

It is shown that also the degree of the ‘squares sequence’ is an atom, and the theory of degrees of infinite sequences with respect to transducibility by finite-state transducers is answered.

The theory of functions and sets of natural numbers

Recursiveness and Computability. Induction. Systems of Equations. Arithmetical Formal Systems. Turing Machines. Flowcharts. Functions as Rules. Arithmetization. Church's Thesis. Basic Recursion…

Elements of Automata Theory

This treatise gives a rigorous account of the topic and illuminates its real meaning by looking at the subject in a variety of ways, including notions of rationality and recognisability.

Conjectures and questions from Gerald Sacks's Degrees of Unsolvability

The important role that the conjectures and questions posed at the end of the two editions of Gerald Sacks's Degrees of Unsolvability have had in the development of recursion theory over the past thirty years are described.

Highlights in infinitary rewriting and lambda calculus

Automatic Sequences - Theory, Applications, Generalizations

This chapter discusses automata, automatic sequences, and other models of computation in number theory and algebra, as well as number systems and numeration systems, and some examples of these models are presented.