We prove that the Karoubi envelope of a shift - defined as the KaroubiĮnvelope of the syntactic semigroup of the language of blocks of the shift. We conjecture that the result holds for all sofic-Dyck shifts.
#SUBSHIFT DISJOINT FROM A GIVEN SUBSHIFT SERIES#
is the generating series of some unambiguous context-free language. We prove that the zeta function of a finite-type-Dyck shift is a computable N-algebraic series, i.e. This proves that the zeta function of all sofic-Dyck shifts is a computable Z-algebraic series. We extend the formula to all sofic-Dyck shifts. An algebraic formula for the zeta function, which counts the periodic sequences of these shifts, can be obtained for sofic-Dyck shifts having a right-resolving presentation. A larger class of constraints, described by sofic-Dyck automata, are the visibly pushdown constraints whose corresponding set of biinfinite sequences are the sofic-Dyck shifts. Regular constraints are described by finite-state automata and the set of bi-infinite constrained sequences are finite-type or sofic shifts. sequences with a predefined set of properties. For the specific case of infinite-alphabet shifts on the lattice N or Z with the usual addition, shifts of variable length can be interpreted as the topological version of variable length Markov chains.Ĭonstrained coding is a technique for converting unrestricted sequences of symbols into constrained sequences, i.e.
This new class is named finitely defined shifts, and the non-finite-type shifts in it are named shifts of variable length. The alternative definition given for shifts of finite type inspires the definition of a new class of shift spaces which intersects with the class of sofic shifts and includes shifts of finite type. Therefore, by examining the core features in the classical definitions of shifts of finite type and sofic shifts, we propose general definitions that can be used in any context. We start showing that the classical definitions of shifts of finite type and sofic shifts, as they are given in the context of finite-alphabet shift spaces on the one-dimensional monoid N or Z with the usual addition, do not fit for shift spaces over infinite alphabet or on other monoids. The aim of this article is to find appropriate definitions for shifts of finite type and sofic shifts in a general context of symbolic dynamics, and to study their properties. We consider partitioned graphs, by which we mean finite strongly connectedĭirected graphs with a partitioned edge set $ $ with the usual sum, shifts of variable length can be interpreted as the topological version of variable length Markov chains.
0 kommentar(er)
