The Syntactic Graph of a Sofic Shift Is Invariant under Shift Equivalence
نویسندگان
چکیده
We define a new invariant for shift equivalence of sofic shifts. This invariant, that we call the syntactic graph of a sofic shift, is the directed acyclic graph of characteristic groups of the non null regular D-classes of the syntactic semigroup of the shift.
منابع مشابه
A categorical invariant of flow equivalence of shifts
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...
متن کاملA 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 کاملA hierarchy of shift equivalent sofic shifts
We 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. We prove that these classes define invariants shift equivalence (and thus for conjugacy). Finally, we...
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 کاملOn Flow Equivalence of Sofic Shifts
The flow equivalence of sofic shifts is examined using results about the structure of the corresponding covers. A canonical cover generalising the left Fischer cover to arbitrary sofic shifts is introduced and used to prove that the left Krieger cover and the past set cover of a sofic shift can be divided into natural layers. These results are used to find the range of a flow invariant and to i...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- IJAC
دوره 16 شماره
صفحات -
تاریخ انتشار 2006