47 research outputs found
1D Effectively Closed Subshifts and 2D Tilings
Michael Hochman showed that every 1D effectively closed subshift can be
simulated by a 3D subshift of finite type and asked whether the same can be
done in 2D. It turned out that the answer is positive and necessary tools were
already developed in tilings theory. We discuss two alternative approaches:
first, developed by N. Aubrun and M. Sablik, goes back to Leonid Levin; the
second one, developed by the authors, goes back to Peter Gacs.Comment: Journ\'ees Automates Cellulaires, Turku : Finland (2010
On Derivatives and Subpattern Orders of Countable Subshifts
We study the computational and structural aspects of countable
two-dimensional SFTs and other subshifts. Our main focus is on the topological
derivatives and subpattern posets of these objects, and our main results are
constructions of two-dimensional countable subshifts with interesting
properties. We present an SFT whose iterated derivatives are maximally complex
from the computational point of view, a sofic shift whose subpattern poset
contains an infinite descending chain, a family of SFTs whose finite subpattern
posets contain arbitrary finite posets, and a natural example of an SFT with
infinite Cantor-Bendixon rank.Comment: In Proceedings AUTOMATA&JAC 2012, arXiv:1208.249
Enumeration Reducibility in Closure Spaces with Applications to Logic and Algebra
In many instances in first order logic or computable algebra, classical
theorems show that many problems are undecidable for general structures, but
become decidable if some rigidity is imposed on the structure. For example, the
set of theorems in many finitely axiomatisable theories is nonrecursive, but
the set of theorems for any finitely axiomatisable complete theory is
recursive. Finitely presented groups might have an nonrecursive word problem,
but finitely presented simple groups have a recursive word problem. In this
article we introduce a topological framework based on closure spaces to show
that many of these proofs can be obtained in a similar setting. We will show in
particular that these statements can be generalized to cover arbitrary
structures, with no finite or recursive presentation/axiomatization. This
generalizes in particular work by Kuznetsov and others. Examples from first
order logic and symbolic dynamics will be discussed at length
Proceedings of JAC 2010. Journées Automates Cellulaires
The second Symposium on Cellular Automata “Journ´ees Automates Cellulaires” (JAC 2010) took place in Turku, Finland, on December 15-17, 2010. The first two conference days were held in the Educarium building of the University of Turku, while the talks of the third day were given onboard passenger ferry boats in the beautiful Turku archipelago, along the route Turku–Mariehamn–Turku. The conference was organized by FUNDIM, the Fundamentals of Computing and Discrete Mathematics research center at the mathematics department of the University of Turku.
The program of the conference included 17 submitted papers that were selected by the international program committee, based on three peer reviews of each paper. These papers form the core of these proceedings. I want to thank the members of the program committee and the external referees for the excellent work that have done in choosing the papers to be presented in the conference. In addition to the submitted papers, the program of JAC 2010 included four distinguished invited speakers: Michel Coornaert (Universit´e de Strasbourg, France), Bruno Durand (Universit´e de Provence, Marseille, France), Dora Giammarresi (Universit` a di Roma Tor Vergata, Italy) and Martin Kutrib (Universit¨at Gie_en, Germany). I sincerely thank the invited speakers for accepting our invitation to come and give a plenary talk in the conference. The invited talk by Bruno Durand was eventually given by his co-author Alexander Shen, and I thank him for accepting to make the presentation with a short notice. Abstracts or extended abstracts of the invited presentations appear in the first part of this volume.
The program also included several informal presentations describing very recent developments and ongoing research projects. I wish to thank all the speakers for their contribution to the success of the symposium. I also would like to thank the sponsors and our collaborators: the Finnish Academy of Science and Letters, the French National Research Agency project EMC (ANR-09-BLAN-0164), Turku Centre for Computer Science, the University of Turku, and Centro Hotel. Finally, I sincerely thank the members of the local organizing committee for making the conference possible.
These proceedings are published both in an electronic format and in print. The electronic proceedings are available on the electronic repository HAL, managed by several French research agencies. The printed version is published in the general publications series of TUCS, Turku Centre for Computer Science. We thank both HAL and TUCS for accepting to publish the proceedings.Siirretty Doriast