31 research outputs found
The syntactic graph of a sofic shift is invariant under shift equivalence
International audienceWe de ne a new invariant for shift equivalence of so fic shifts. This invariant, that we call the syntactic graph of a so fic shift, is the directed acyclic graph of characteristic groups of the non null regular D-classes of the syntactic semigroup of the shift
A new algebraic invariant for weak equivalence of sofic subshifts
It is studied how taking the inverse image by a sliding block code
affects the syntactic semigroup of a sofic subshift. Two independent approaches are
used: ζ-semigroups as recognition structures for sofic subshifts, and relatively free
profinite semigroups. A new algebraic invariant is obtained for weak equivalence
of sofic subshifts, by determining which classes of sofic subshifts naturally defined
by pseudovarieties of finite semigroups are closed under weak equivalence. Among
such classes are the classes of almost finite type subshifts and aperiodic subshifts.
The algebraic invariant is compared with other robust conjugacy invariants.Research programme AutoMathA of ESF; Pessoa bilateral project Egide/Grices 11113YM "Automata, profinite semigroups and symbolic dynamics"; FCT, grant SFRH/BD/24200/2005; POCI 2010; FS
A new algebraic invariant for weak equivalence of sofic subshifts
It is studied how taking the inverse image by a sliding block code
affects the syntactic semigroup of a sofic subshift. Two independent approaches are
used: ζ-semigroups as recognition structures for sofic subshifts, and relatively free
profinite semigroups. A new algebraic invariant is obtained for weak equivalence
of sofic subshifts, by determining which classes of sofic subshifts naturally defined
by pseudovarieties of finite semigroups are closed under weak equivalence. Among
such classes are the classes of almost finite type subshifts and aperiodic subshifts.
The algebraic invariant is compared with other robust conjugacy invariants.Research programme AutoMathA of ESF; Pessoa bilateral project Egide/Grices 11113YM "Automata, profinite semigroups and symbolic dynamics"; FCT, grant SFRH/BD/24200/2005; POCI 2010; FS
A hierarchy of irreducible sofic shifts
International audienceWe define new subclasses of the class of irreducible sofic shifts. These classes form an infinite hierarchy where the lowest class is the class of almost finite type shifts introduced by B. Marcus. We give effective characterizations of these classes with the syntactic semigroups of the shifts
On subshift presentations
We consider partitioned graphs, by which we mean finite strongly connected
directed graphs with a partitioned edge set . With additionally given a relation between
the edges in and the edges in , and denoting
the vertex set of the graph by , we speak of an an -graph . From -graphs we construct semigroups (with zero) that we call
-graph semigroups. We describe a method of presenting subshifts
by means of suitably structured labelled directed graphs with vertex set , edge set , and a label
map that asigns to the edges in labels in an -graph
semigroup . We call the presented subshift an -presentation.
We introduce a Property and a Property (c), tof subshifts, and we
introduce a notion of strong instantaneity. Under an assumption on the
structure of the -graphs we show for strongly instantaneous
subshifts with Property and associated semigroup , that Properties and (c) are
necessary and sufficient for the existence of an -presentation, to which the
subshift is topologically conjugate,Comment: 33 page
Profinite Groups Associated to Sofic Shifts are Free
We show that the maximal subgroup of the free profinite semigroup associated
by Almeida to an irreducible sofic shift is a free profinite group,
generalizing an earlier result of the second author for the case of the full
shift (whose corresponding maximal subgroup is the maximal subgroup of the
minimal ideal). A corresponding result is proved for certain relatively free
profinite semigroups. We also establish some other analogies between the kernel
of the free profinite semigroup and the \J-class associated to an irreducible
sofic shift