Pseudovarieties Defining Classes of Sofic Subshifts Closed for Taking Shift Equivalent Subshifts
نویسندگان
چکیده
For a pseudovariety V of ordered semigroups, let S (V) be the class of sofic subshifts whose syntactic semigroup lies in V. It is proved that if V contains Sl− then S (V∗D) is closed for taking shift equivalent subshifts, and conversely, if S (V) is closed for taking conjugate subshifts then V contains LSl− and S (V) = S (V∗D). Almost finite type subshifts are characterized as the irreducible elements of S (LInv), which gives a new proof that the class of almost finite type subshifts is closed for taking shift equivalent subshifts.
منابع مشابه
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 d...
متن کاملTuring Degree Spectra of Minimal Subshifts
Subshifts are shift invariant closed subsets of Σ d , minimal subshifts are subshifts in which all points contain the same patterns. It has been proved by Jeandel and Vanier that the Turing degree spectra of nonperiodic minimal subshifts always contain the cone of Turing degrees above any of its degree. It was however not known whether each minimal subshift’s spectrum was formed of exactly one ...
متن کاملConjugacy Invariants of Subshifts: an Approach from Profinite Semigroup Theory
It is given a structural conjugacy invariant in the set of pseudowords whose finite factors are factors of a given subshift. Some profinite semigroup tools are developed for this purpose. With these tools a shift equivalence invariant of sofic subshifts is obtained, improving an invariant introduced by Béal, Fiorenzi and Perrin using different techniques. This new invariant is used to prove tha...
متن کاملTEL-AVIV UNIVERSITY RAYMOND AND BEVERLY SACKLER FACULTY OF EXACT SCIENCES SCHOOL OF MATHEMATICAL SCIENCES Tail Invariant Measures of The Dyck-Shift and Non-Sofic Systems
Among the most familiar systems in symbolic dynamics are the subshifts of finite type, or SFT’s for short. SFT’s are relatively easy to analyze, and have many pleasant properties such as intrinsic ergodicity and unique ergodicity with respect to the tail. A larger class, which has the desirable property of being closed under factors, is that of sofic systems. This class of systems retains many ...
متن کاملSubshifts and Logic: Back and Forth
We study the Monadic Second Order (MSO) Hierarchy over colourings of the discrete plane, and draw links between classes of formula and classes of subshifts. We give a characterization of existential MSO in terms of projections of tilings, and of universal sentences in terms of combinations of “pattern counting” subshifts. Conversely, we characterise logic fragments corresponding to various clas...
متن کامل