Related papers: Sofic-Dyck shifts
A decomposition theorem for the Lind zeta function of a reversal system $(X, T, R)$ of finite order is established. A reversal system can be regarded as an action of a certain group $G$ on $X$. To establish an explicit formula for the Lind…
Inspired by a recent novel work of Good and Meddaugh, we establish fundamental connections between shadowing, finite order shifts, and ultrametric complete spaces. We develop a theory of shifts of finite type for infinite alphabets. We call…
In this article we extend the theory of shift-invariant spaces to the context of LCA groups. We introduce the notion of H-invariant space for a countable discrete subgroup H of an LCA group G, and show that the concept of range function and…
The zeta-dimension of a set A of positive integers is the infimum s such that the sum of the reciprocals of the s-th powers of the elements of A is finite. Zeta-dimension serves as a fractal dimension on the positive integers that extends…
We define supersymmetric zeta functions and supersymmetric determinants, which can reveal spectral properties complementary to those captured by the supersymmetric indices. They play a crucial role in analyzing the Cardy-like behaviors of…
In this work we characterize those shift spaces which can support a 1-block quasi-group operation and show the analogous of Kitchens result: any such shift is conjugated to a product of a full shift with a finite shift. Moreover, we prove…
A complete characterization of parabolic self-maps of finite shift is given in terms of their Herglotz's representation. This improves a previous result due to Contreras, D\'iaz-Madrigal, and Pommerenke. We also derive some consequences for…
In this paper we further develop the theory of one sided shift spaces over infinite alphabets, characterizing one-step shifts as edge shifts of ultragraphs and partially answering a conjecture regarding shifts of finite type (we show that…
We study expression learning problems with syntactic restrictions and introduce the class of finite-aspect checkable languages to characterize symbolic languages that admit decidable learning. The semantics of such languages can be defined…
Higher-order pushdown systems and ground tree rewriting systems can be seen as extensions of suffix word rewriting systems. Both classes generate infinite graphs with interesting logical properties. Indeed, the model-checking problem for…
In this paper, we introduce and study the Dirichlet series enumerating (proper) equivalence classes of full rank subforms/sublattices of a given quadratic form/lattice, focusing on the positive definite binary case. We obtain formulas…
In this paper, we explore the properties of zeta functions associated with infinite graphs of groups that arise as quotients of cuspidal tree-lattices, including all non-uniform arithmetic quotients of the tree of rank one Lie groups over…
We define a new weighted zeta function for a finite graph and obtain its determinant expression. This result gives the characteristic polynomial of the transition matrix of the Szegedy walk on a graph.
We consider a SDE with a smooth multiplicative non-degenerate noise and a possibly unbounded Holder continuous drift term. We prove existence of a global flow of diffeomorphisms by means of a special transformation of the drift of…
We define a pair of simple combinatorial operations on subshifts, called existential and universal extensions, and study their basic properties. We prove that the existential extension of a sofic shift by another sofic shift is always…
Fermi-Dirac and Bose-Einstein integral functions are of importance not only in quantum statistics but for their mathematical properties, in themselves. Here, we have extended these functions by introducing an extra parameter in a way that…
The $S$-gap shifts have a dynamically and combinatorially rich structure. Dynamical properties of the $S$-gap shift can be related to the properties of the set $S$. This interplay is particularly interesting when $S$ is not syndetic such as…
We conceive finite automata as dynamical systems on discontinuum and investigate their factors. Factors of finite automata include many well-known simple dynamical systems, e.g. hyperbolic systems and systems with finite attractors. In the…
Centering theory posits a discourse center, a distinguished discourse entity that is the topic of a discourse. A simplified version of this theory is developed in a Dynamic Semantics framework. In the resulting system, the mechanism of…
One of the main claims of the paper is that Dirac's calculus and broader theories of physics can be treated as theories written in the language of Continuous Logic. Establishing its true interpretation (model) is a model theory problem. The…