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The chain relation in sofic subshifts [article]

Alexandr Kazda
2009 arXiv   pre-print
Using G/_≈ we describe first the chain relation in Σ, then characterise chain-transitive sofic subshifts, chain-mixing sofic subshifts and finally the attractors of the subshift dynamic system.  ...  The paper gives a characterisation of the chain relation of a sofic subshift. Every sofic subshift Σ can be described by a labelled graph G.  ...  The chain relation is an important characteristic of subshifts as well as of dynamical systems in general.  ... 
arXiv:0911.5475v1 fatcat:fhclg2zmv5abxakfbjdbkktkny

Symbolic dynamics and semigroup theory [article]

Alfredo Costa
2018 arXiv   pre-print
In this article we survey some developments on this connection, since when it was noticed in an article by Almeida, published in the CIM bulletin, in 2003.  ...  A major motivation for the development of semigroup theory was, and still is, its applications to the study of formal languages.  ...  Acknowledgments Work partially supported by the Centre for Mathematics of the University of Coimbra -UID/MAT/00324/2013, funded by the Portuguese Government through FCT/MCTES and co-funded by the European  ... 
arXiv:1811.04013v1 fatcat:bhek7jct5vehxje7hfcvwvo4ku

Some sofic shifts cannot commute with nonwandering shifts of finite type

Mike Boyle
2004 Illinois Journal of Mathematics  
We show T cannot be a strictly sofic almost Markov shift. Also included is an example of D. Fiebig, a reducible SFT with an expansive automorphism which is not SFT.  ...  In Example A.1, the nonSFT expansive automorphism T is totally chain transitive; as the union of two SFTs, it is also an almost Markov sofic shift.  ...  A sofic shift is a subshift which is the image of an SFT under a block code. We will say a subshift is irreducible if it has a dense forward orbit.  ... 
doi:10.1215/ijm/1258138511 fatcat:dutyj4ykwfaabeab436sx7z2xq

Topological conjugacy for sofic systems

Masakazu Nasu
1986 Ergodic Theory and Dynamical Systems  
We prove that any topological conjugacy between subshifts is decomposed into the product of'bipartite codes', and obtain a natural generalization of Williams' theorem to sofic systems: two sofic systems  ...  to Fischer covers holds for transitive sofic systems.  ...  It is well known that a subshift is a sofic system iff it is the image of a factor map of (0,0) type from some topological Markov chain.  ... 
doi:10.1017/s0143385700003448 fatcat:swovuhrnwrfibmhlargohijaji

On Derivatives and Subpattern Orders of Countable Subshifts

Ville Salo, Ilkka Törmä
2012 Electronic Proceedings in Theoretical Computer Science  
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  ...  We study the computational and structural aspects of countable two-dimensional SFTs and other subshifts.  ...  We solve this in the positive for two-dimensional sofic shifts, by finding such a chain in a countable sofic shift.  ... 
doi:10.4204/eptcs.90.3 fatcat:u7noni6yv5cutfxzs3mtgms4ly

Chains, entropy, coding

Karl Petersen
1986 Ergodic Theory and Dynamical Systems  
Factors of some of these chains have entropy equal to the growth rate of the number of periodic orbits, even though they contain no subshifts of finite type with positive entropy; others are almost sofic-they  ...  Certain restricted random walks which arise in a problem in magnetic recording provide interesting examples of chains.  ...  ( 5 ) 5 A(c, 0) is the 'chain above' the subshift 2(c, 8), as in [3].  ... 
doi:10.1017/s014338570000359x fatcat:ahnj7llapjhhnjtedr5v5jctne

Extender sets and multidimensional subshifts

2014 Ergodic Theory and Dynamical Systems  
In this paper, we consider a$\mathbb{Z}^{d}$extension of the well known fact that subshifts with only finitely many follower sets are sofic.  ...  However, most proofs of that result use the fact that the number of words of length$n$in a$\mathbb{Z}$subshift is non-decreasing in$n$, and we present an example (due to Martin Delacourt) which shows that  ...  There are many relations between properties of X and the behavior of N S (X).  ... 
doi:10.1017/etds.2014.71 fatcat:ez5x5fabvrc2xfudl5xqj2l66q

Page 7521 of Mathematical Reviews Vol. , Issue 95m [page]

1995 Mathematical Reviews  
In particular, they show that if a sofic shift has unique minimal presentation, then it is a subshift of finite type.  ...  This paper relates the dynamics of homeomorphisms in the two- parameter Hénon family to the dynamics of maps of the interval in the one-parameter quadratic family.  ... 

Category theory of symbolic dynamics

Ville Salo, Ilkka Törmä
2015 Theoretical Computer Science  
We study the central objects of symbolic dynamics, that is, subshifts and block maps, from the perspective of basic category theory, and present several natural categories with subshifts as objects and  ...  Existing definitions in category theory suggest interesting new problems for block maps.  ...  The first part of Example 8 is due to Silvio Capobianco, and was communicated to us by Guillon, although our proof is different. References  ... 
doi:10.1016/j.tcs.2014.10.023 fatcat:vjn4rbikbjc3bagnfzxz2k7dqe

Computational Aspects of Cellular Automata on Countable Sofic Shifts [chapter]

Ville Salo, Ilkka Törmä
2012 Lecture Notes in Computer Science  
We investigate the computational properties of cellular automata on countable (equivalently, zero entropy) sofic shifts with an emphasis on nilpotency, periodicity, and asymptotic behavior.  ...  We present computational results including the decidability of nilpotency and periodicity, the undecidability of stability of the limit set, and the existence of a Π 0 1 -complete limit set and a Σ 0 3  ...  Acknowledgements We'd like to thank Jarkko Kari for pointing out that Lemma 3 holds even in the case of a general subshift, Pierre Guillon for his useful comments, in particular on the last section, and  ... 
doi:10.1007/978-3-642-32589-2_67 fatcat:pqwezi4tv5cbzih3askyjkueta

Classification of sofic projective subdynamics of multidimensional shifts of finite type

Ronnie Pavlov, Michael Schraudner
2014 Transactions of the American Mathematical Society  
with the uniform filling property (UFP) are always sofic and we exhibit a class of non-sofic Z subshifts which are not the subdynamics of any Z d SFT.  ...  Finally, we prove that the union of Z k subshifts all of which are realizable in Z d SFTs is again realizable when it contains at least two periodic points, that the projective subdynamics of Z 2 SFTs  ...  In addition, it is possible to see some relations between known conditions which guarantee stable realization of a Z sofic S in both setups, in the sense that Maass's condition of containing a "receptive  ... 
doi:10.1090/s0002-9947-2014-06259-4 fatcat:wrowsd4rpzdevac66gfolaabqm

Degenerated ground-states in a spin chain with pair interactions: a characterization by symbolic dynamics

L A Corona, R Salgado-García
2016 Journal of Statistical Mechanics: Theory and Experiment  
Particularly we found that the set ground- state configurations defines what in symbolic dynamics is called sofic shift space.  ...  In this note we study a class of one-dimensional Ising chain having a highly degenerated set of ground-state configurations.  ...  Acknowledgements The authors thanks CONACyT for financial support through Grant No. CB-2012-01-183358. Degenerated ground-states in a class of 1D Ising-like models  ... 
doi:10.1088/1742-5468/aa4e5f fatcat:txodqfxbcnatfhzcwsqpxldrhm

Constructions with Countable Subshifts of Finite Type [article]

Ville Salo, Ilkka Törmä
2013 arXiv   pre-print
When possible, we make these constructions deterministic, and ensure the sets of rows are very simple as one-dimensional subshifts.  ...  subpattern poset contains an infinite descending chain and a countable SFT whose subpattern poset contains all finite posets.  ...  improved the paper.  ... 
arXiv:1310.0654v1 fatcat:33jxn6bnlre3hh4eofxhgtpfey

On the density of periodic configurations in strongly irreducible subshifts

Tullio Ceccherini-Silberstein, Michel Coornaert
2012 Nonlinearity  
We also introduce a class of subshifts X ⊂ A^, including all strongly irreducible subshifts and all irreducible sofic subshifts, in which periodic configurations are dense.  ...  The density of periodic configurations implies in particular that every injective endomorphism of X is surjective and that the group of automorphisms of X is residually finite.  ...  For example, the even subshift X ⊂ {0, 1} Z (i.e., the subshift formed by all bi-infinite sequences of 0s and 1s in which every chain of 1s which is bounded by two 0s has even length) is sofic.  ... 
doi:10.1088/0951-7715/25/7/2119 fatcat:xqrhlng6dzbpxn3jq2zpgqexgu

Page 2893 of Mathematical Reviews Vol. , Issue 88f [page]

1988 Mathematical Reviews  
Not only must the same type of matrix system be solved but it must be done in a way that respects the labeling in the canonical graph (the Krieger or Fisher cover) for a sofic system. R. L.  ...  Adler (1-IBM) 88f:28019 28D20 54H20 58F11 Zargaryan, A.S. (2-MOSC) A variational principle for the topological pressure in the case of a Markov chain with a countable number of states. (Russian) Mat.  ... 
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