scholarly journals Quantifier extensions of multidimensional sofic shifts

2015 ◽  
Vol 143 (11) ◽  
pp. 4775-4790 ◽  
Author(s):  
Ilkka Törmä
Keyword(s):  
Sofic Shifts

scholarly journals Multi-dimensional maps with infinite invariant measures and countable state sofic shifts

1995 ◽  
Vol 6 (3) ◽  
pp. 355-383 ◽  
Author(s):  
Michiko Yuri
Keyword(s):  
Invariant Measures ◽  
Sofic Shifts ◽  
Countable State

scholarly journals Subsystem entropy for ℤd sofic shifts

2006 ◽  
Vol 17 (3) ◽  
pp. 353-359 ◽  
Author(s):  
Angela Desai
Keyword(s):  
Sofic Shifts

Sofic Shifts via Conley Index Theory: Computing Lower Bounds on Recurrent Dynamics for Maps

2019 ◽  
Vol 18 (3) ◽  
pp. 1610-1642
Author(s):  
Sarah Day ◽  
Rafael Frongillo
Keyword(s):  
Lower Bounds ◽  
Index Theory ◽  
Conley Index ◽  
Conley Index Theory ◽  
Sofic Shifts

scholarly journals Multidimensional sofic shifts without separation and their factors

2010 ◽  
Vol 362 (9) ◽  
pp. 4617-4653 ◽  
Author(s):  
Mike Boyle ◽  
Ronnie Pavlov ◽  
Michael Schraudner
Keyword(s):  
Sofic Shifts

scholarly journals -ALGEBRAS ASSOCIATED WITH LAMBDA-SYNCHRONIZING SUBSHIFTS AND FLOW EQUIVALENCE

2013 ◽  
Vol 95 (2) ◽  
pp. 241-265 ◽  
Author(s):  
KENGO MATSUMOTO
Keyword(s):  
Algebraic Structure ◽  
Isomorphism Class ◽  
Cartan Subalgebra ◽  
Sofic Shift ◽  
Sofic Shifts ◽  
Flow Equivalence ◽  
Graph System

AbstractThe class of $\lambda $-synchronizing subshifts generalizes the class of irreducible sofic shifts. A $\lambda $-synchronizing subshift can be presented by a certain $\lambda $-graph system, called the $\lambda $-synchronizing $\lambda $-graph system. The $\lambda $-synchronizing $\lambda $-graph system of a $\lambda $-synchronizing subshift can be regarded as an analogue of the Fischer cover of an irreducible sofic shift. We will study algebraic structure of the ${C}^{\ast } $-algebra associated with a $\lambda $-synchronizing $\lambda $-graph system and prove that the stable isomorphism class of the ${C}^{\ast } $-algebra with its Cartan subalgebra is invariant under flow equivalence of $\lambda $-synchronizing subshifts.

Core dimension group constraints for factors of sofic shifts

1993 ◽  
Vol 13 (1) ◽  
pp. 213-224 ◽  
Author(s):  
Paul Trow ◽  
Susan Williams
Keyword(s):  
Characteristic Polynomial ◽  
The Core ◽  
Sofic Shift ◽  
Dimension Group ◽  
Core Matrix ◽  
Sofic Shifts ◽  
Factor Maps

AbstractWe give constraints on the existence of factor maps between sofic shifts. These constraints yield examples of sofic shifts of entropy lognwhich do not factor onto the fulln-shift. We also show that any prime which divides the degree of an endomorphism of a sofic shift must divide the non-leading coefficients of the characteristic polynomial of the core matrix of the shift.

scholarly journals Normal amenable subgroups of the automorphism group of sofic shifts

2020 ◽  
pp. 1-14
Author(s):  
KITTY YANG
Keyword(s):  
Automorphism Group ◽  
Finite Type ◽  
Higher Dimensions ◽  
Two Dimensional ◽  
Shift Of Finite Type ◽  
Sofic Shift ◽  
Sofic Shifts ◽  
Amenable Subgroup

Let $(X,\unicode[STIX]{x1D70E})$ be a transitive sofic shift and let $\operatorname{Aut}(X)$ denote its automorphism group. We generalize a result of Frisch, Schlank, and Tamuz to show that any normal amenable subgroup of $\operatorname{Aut}(X)$ must be contained in the subgroup generated by the shift. We also show that the result does not extend to higher dimensions by giving an example of a two-dimensional mixing shift of finite type due to Hochman whose automorphism group is amenable and not generated by the shift maps.

scholarly journals A categorical invariant of flow equivalence of shifts

2014 ◽  
Vol 36 (2) ◽  
pp. 470-513 ◽  
Author(s):  
ALFREDO COSTA ◽  
BENJAMIN STEINBERG
Keyword(s):  
Analogous Result ◽  
Mild Conditions ◽  
Equivalence Of Categories ◽  
Natural Equivalence ◽  
Sofic Shifts ◽  
Flow Equivalence ◽  
Flow Invariance ◽  
Natural Sense

We prove that the Karoubi envelope of a shift—defined as the Karoubi envelope of the syntactic semigroup of the language of blocks of the shift—is, up to natural equivalence of categories, an invariant of flow equivalence. More precisely, we show that the action of the Karoubi envelope on the Krieger cover of the shift is a flow invariant. An analogous result concerning the Fischer cover of a synchronizing shift is also obtained. From these main results, several flow equivalence invariants—some new and some old—are obtained. We also show that the Karoubi envelope is, in a natural sense, the best possible syntactic invariant of flow equivalence of sofic shifts. Another application concerns the classification of Markov–Dyck and Markov–Motzkin shifts: it is shown that, under mild conditions, two graphs define flow equivalent shifts if and only if they are isomorphic. Shifts with property ($\mathscr{A}$) and their associated semigroups, introduced by Wolfgang Krieger, are interpreted in terms of the Karoubi envelope, yielding a proof of the flow invariance of the associated semigroups in the cases usually considered (a result recently announced by Krieger), and also a proof that property ($\mathscr{A}$) is decidable for sofic shifts.

scholarly journals Asymptotic randomization of sofic shifts by linear cellular automata

2006 ◽  
Vol 26 (04) ◽  
pp. 1177 ◽  
Author(s):  
MARCUS PIVATO ◽  
REEM YASSAWI
Keyword(s):  
Cellular Automata ◽  
Sofic Shifts

Lattice invariants for sofic shifts

1991 ◽  
Vol 11 (4) ◽  
pp. 787-801 ◽  
Author(s):  
Susan Williams
Keyword(s):  
Finite Type ◽  
Necessary Conditions ◽  
Shift Of Finite Type ◽  
Sofic Shift ◽  
Dimension Group ◽  
Sofic Shifts ◽  
Factor Map ◽  
Factor Maps

AbstractTo a factor map φ from an irreducible shift of finite type ΣAto a sofic shiftS, we associate a subgroup of the dimension group (GA, Â) which is an invariant of eventual conjugacy for φ. This invariant yields new necessary conditions for the existence of factor maps between equal entropy sofic shifts.

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