On Uniformly Recurrent Morphic Sequences
نویسندگان
چکیده
In the paper we mainly deal with two well-known types of in nite words: morphic and uniformly recurrent (=almost periodic). We discuss the problem of nding criterion of uniform recurrence for morphic sequences and give e ective polynomial-time such criterion in two particular cases: pure morphic sequences and automatic sequences. We also prove that factor complexity of arbitrary uniformly recurrent morphic sequence is at most linear.
منابع مشابه
Decidability of Uniform Recurrence of Morphic Sequences
We prove that the uniform recurrence of morphic sequences is decidable. For this we show that the number of derived sequences of uniformly recurrent morphic sequences is bounded. As a corollary we obtain that uniformly recurrent morphic sequences are primitive substitutive sequences.
متن کاملOn Almost Periodicity Criteria for Morphic Sequences in Some Particular Cases
In some particular cases we give criteria for morphic sequences to be almost periodic (=uniformly recurrent). Namely, we deal with fixed points of non-erasing morphisms and with automatic sequences. In both cases a polynomial-time algorithm solving the problem is found. A result more or less supporting the conjecture of decidability of the general problem is given.
متن کاملAlmost Rich Words as Morphic Images of Rich Words
We focus on Θ-rich and almost Θ-rich words over a finite alphabet A, where Θ is an involutive antimorphism over A∗. We show that any recurrent almost Θ-rich word u is an image of a recurrent Θ′-rich word under a suitable morphism, where Θ′ is also an involutive antimorphism. Moreover, if the word u is uniformly recurrent, we show that Θ′ can be set to the reversal mapping. We also treat one spe...
متن کاملOn Subword Complexity of Morphic Sequences
We study structure of pure morphic and morphic sequences and prove the following result: the subword complexity of arbitrary morphic sequence is either Θ(n) for some k ∈ N, or is
متن کاملOn GCD-morphic sequences
This note is a response to one of the problems posed by Kwa´sniewski in [1, 2], see also [3] i.e. GCD-morphic Problem III. We show that any GCD-morphic sequence F is at the point product of primary GCD-morphic sequences and any GCD-morphic sequence is encoded by natural number valued sequence satisfying condition (C1). The problem of general importance-for example in number theory was formulate...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Int. J. Found. Comput. Sci.
دوره 20 شماره
صفحات -
تاریخ انتشار 2009