A4 Refereed article in a conference publication
Degrees of infinite words, polynomials and atoms
Authors: Jörg Endrullis, Juhani Karhumäki, Jan Willem Klop, Aleksi Saarela
Editors: Srečko Brlek, Christophe Reutenauer
Conference name: International Conference on Developments in Language Theory
Publication year: 2016
Book title : Developments in Language Theory: 20th International Conference, DLT 2016, Montréal, Canada, July 25-28, 2016, Proceedings
Series title: Lecture Notes in Computer Science
Number in series: 9840
Volume: 9840
First page : 164
Last page: 176
Number of pages: 13
ISBN: 978-3-662-53131-0
eISBN: 978-3-662-53132-7
ISSN: 0302-9743
DOI: https://doi.org/10.1007/978-3-662-53132-7_14(external)
Our objects of study are finite state
transducers and their power for transforming infinite words. Infinite
sequences of symbols are of paramount importance in a wide range of
fields, from formal languages to pure mathematics and physics. While
finite automata for recognising and transforming languages are
well-understood, very little is known about the power of automata to
transform infinite words.
We use methods
from linear algebra and analysis to show that there is an infinite
number of atoms in the transducer degrees, that is, minimal non-trivial
degrees.
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