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The chain relation in sofic subshifts
[article]

2009
*
arXiv
*
pre-print

Using G/_≈ we describe first

arXiv:0911.5475v1
fatcat:fhclg2zmv5abxakfbjdbkktkny
*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. ...##
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Symbolic dynamics and semigroup theory
[article]

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 ...

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Some sofic shifts cannot commute with nonwandering shifts of finite type

2004
*
Illinois Journal of Mathematics
*

We show T cannot be a strictly

doi:10.1215/ijm/1258138511
fatcat:dutyj4ykwfaabeab436sx7z2xq
*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. ...##
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Topological conjugacy for sofic systems

1986
*
Ergodic Theory and Dynamical Systems
*

We prove that any topological conjugacy between

doi:10.1017/s0143385700003448
fatcat:swovuhrnwrfibmhlargohijaji
*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*. ...##
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On Derivatives and Subpattern Orders of Countable Subshifts

2012
*
Electronic Proceedings in Theoretical Computer Science
*

We present an SFT whose iterated derivatives are maximally complex from

doi:10.4204/eptcs.90.3
fatcat:u7noni6yv5cutfxzs3mtgms4ly
*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. ...##
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Chains, entropy, coding

1986
*
Ergodic Theory and Dynamical Systems
*

Factors of some of these

doi:10.1017/s014338570000359x
fatcat:ahnj7llapjhhnjtedr5v5jctne
*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]. ...##
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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). ...

##
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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. ...

##
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Category theory of symbolic dynamics

2015
*
Theoretical Computer Science
*

We study

doi:10.1016/j.tcs.2014.10.023
fatcat:vjn4rbikbjc3bagnfzxz2k7dqe
*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 ...##
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Computational Aspects of Cellular Automata on Countable Sofic Shifts
[chapter]

2012
*
Lecture Notes in Computer Science
*

We investigate

doi:10.1007/978-3-642-32589-2_67
fatcat:pqwezi4tv5cbzih3askyjkueta
*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 ...##
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Classification of sofic projective subdynamics of multidimensional shifts of finite type

2014
*
Transactions of the American Mathematical Society
*

with

doi:10.1090/s0002-9947-2014-06259-4
fatcat:wrowsd4rpzdevac66gfolaabqm
*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 ...##
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Degenerated ground-states in a spin chain with pair interactions: a characterization by symbolic dynamics

2016
*
Journal of Statistical Mechanics: Theory and Experiment
*

Particularly we found that

doi:10.1088/1742-5468/aa4e5f
fatcat:txodqfxbcnatfhzcwsqpxldrhm
*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 ...##
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Constructions with Countable Subshifts of Finite Type
[article]

2013
*
arXiv
*
pre-print

When possible, we make these constructions deterministic, and ensure

arXiv:1310.0654v1
fatcat:33jxn6bnlre3hh4eofxhgtpfey
*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. ...##
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On the density of periodic configurations in strongly irreducible subshifts

2012
*
Nonlinearity
*

We also introduce a class of

doi:10.1088/0951-7715/25/7/2119
fatcat:xqrhlng6dzbpxn3jq2zpgqexgu
*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*. ...##
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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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