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On Factor Universality in Symbolic Spaces

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Mathematical Foundations of Computer Science 2010 (MFCS 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6281))

Abstract

The study of factoring relations between subshifts or cellular automata is central in symbolic dynamics. Besides, a notion of intrinsic universality for cellular automata based on an operation of rescaling is receiving more and more attention in the literature. In this paper, we propose to study the factoring relation up to rescalings, and ask for the existence of universal objects for that simulation relation.

In classical simulations of a system S by a system T, the simulation takes place on a specific subset of configurations of T depending on S (this is the case for intrinsic universality). Our setting, however, asks for every configurations of T to have a meaningful interpretation in S. Despite this strong requirement, we show that there exists a cellular automaton able to simulate any other in a large class containing arbitrarily complex ones. We also consider the case of subshifts and, using arguments from recursion theory, we give negative results about the existence of universal objects in some classes.

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Authors and Affiliations

  1. LAMA, (UMR 5127 — CNRS, Université de Savoie), Campus Scientifique, 73376, Le Bourget-du-lac cedex, France

    Laurent Boyer & Guillaume Theyssier

Authors
  1. Laurent Boyer
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  2. Guillaume Theyssier
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Editors and Affiliations

  1. Falculty of Informatics, Masaryk University, Botanicka 68a, 602 00, Brno, Czech Republic

    Petr Hliněný

  2. Faculty of Informatics, Masaryk University, Botanicka 68a, 602 00, Brno, Czech Republic

    Antonín Kučera

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Boyer, L., Theyssier, G. (2010). On Factor Universality in Symbolic Spaces. In: Hliněný, P., Kučera, A. (eds) Mathematical Foundations of Computer Science 2010. MFCS 2010. Lecture Notes in Computer Science, vol 6281. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15155-2_20

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  • DOI: https://doi.org/10.1007/978-3-642-15155-2_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15154-5

  • Online ISBN: 978-3-642-15155-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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