Related papers: Characterizing 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 $\Theta(n^{1+1/k})$ for some $k\in\mathbb N$, or is $O(n \log n)$.

The vertices of a finite state system are usually a subset of the natural numbers. Most algorithms relative to these systems only use this fact to select vertices. For infinite state systems, however, the situation is different: in…

We investigate the extent to which Linear Temporal Logic (LTL) formulas can be uniquely characterized by a finite set of labeled examples. We consider different types of examples, ranging from finite words to transfinite words, as well as…

We study those automatic sequences which are produced by an automaton whose underlying graph is the Cayley graph of a finite group. For $2$-automatic sequences, we find a characterization in terms of what we call homogeneity, and among…

This paper contains results related to synthesis and presentation of abstract automata by fragments of behaviour and investigates the structure of the classes of finite connected initial output-less automata specified by systems of defining…

We define a family of meta-Fibonacci sequences where the order of the of recursion at stage n is a variable r(n), and the n^{th} term of a sequence is the sum of the previous r(n) terms. For the terms of any such sequence, we give upper and…

This paper introduces an abstract notion of fragments of monadic second-order logic. This concept is based on purely syntactic closure properties. We show that over finite words, every logical fragment defines a lattice of languages with…

We define a class of sequences ${a_n}$ by $a_1=a$ and $a_{n+1}=P(a_n)$, where $P(x)$ is a polynomial with real coefficients. We then find out for which values $a$ and for which polynomials $P(x)$ these sequences will be constant after a…

We produce a long exact sequence whose terms are unit groups of associative algebras that behave as inner automorphisms of a given tensor. Our sequence generalizes known sequences for associative and non-associative algebras. In a manner…

Autostackability for finitely presented groups is a topological property of the Cayley graph combined with formal language theoretic restrictions, that implies solvability of the word problem. The class of autostackable groups is known to…

We consider limit probabilities of first order properties in random graphs with a given degree sequence. Under mild conditions on the degree sequence, we show that the closure set of limit probabilities is a finite union of closed…

We provide an ergodic theory framework to study statistical properties of smooth sequences over the odd alphabet {1, 3}. The arithmetic nature of this alphabet yields a partition of the subshift of smooth sequences based on their local…

Sequence classification is the task of predicting a class label given a sequence of observations. In many applications such as healthcare monitoring or intrusion detection, early classification is crucial to prompt intervention. In this…

Nested (or meta-Fibonacci) recurrences, such as the recurrence used to define Hofstadter's Q-sequence, along with the digit-based recurrences that underlie automatic sequences are of interest from both number-theoretic and combinatorial…

Sets with atoms serve as an alternative to ZFC foundations for mathematics, where some infinite, though highly symmetric sets, behave in a finitistic way. Therefore, one can try to carry over analysis of the classical algorithms from finite…

In this chapter we survey two topics that have recently been investigated in frame theory. First, we give an overview of the class of scalable frames. These are (finite) frames with the property that each frame vector can be rescaled in…

We define a fragment of monadic infinitary second-order logic corresponding to an abstract separation property. We use this to define the concept of a separation subclass. We use model theoretic techniques and games to show that separation…

We consider forkable regular expressions, which enrich regular expressions with a fork operator, to establish a formal basis for static and dynamic analysis of the communication behavior of concurrent programs. We define a novel…

In this paper we determine the representation type of some algebras of infinite matrices continuously controlled at infinity by a compact metrizable space. We explicitly classify their finitely presented modules in the finite and tame…

We define the arithmetic self-similarity (AS) of a one-sided infinite sequence sigma to be the set of arithmetic progressions through sigma which are a vertical shift of sigma. We study the AS of several famlies of sequences, viz.…