Related papers: A note on Automatic Baire property
We prove that the lower density operator associated with the Baire category density points in the real line has Borel values of class $\pmb \Pi^0_3$ which is analogous to the measure case. We also introduce the notion of the Baire category…
In the paper a new sufficient condition for the Aubin property to a class of parameterized variational systems is derived. In these systems the constraints depend both on the parameter as well as on the decision variable itself and they…
We examine the characteristic features of reversible and quantum computations in the presence of supplementary external information, known as advice. In particular, we present a simple, algebraic characterization of languages recognized by…
A classical theorem of Hurewicz characterizes spaces with the Hurewicz covering property as those having bounded continuous images in the Baire space. We give a similar characterization for spaces X which have the Hurewicz property…
In this article, we shall explore the constructions of Bernstein sets, and prove that every Bernstein set is nonmeasurable and doesn't have the property of Baire. We shall also prove that Bernstein sets don't have the perfect set property.
Affine automata provide a finite-state computational model that preserves the linear-algebraic structure of quantum computation while operating entirely over the reals. Recent work has shown that affine automata can far surpass classical…
Let M be a connected Riemannian manifold and let D be a Dirac type operator acting on smooth compactly supported sections in a Hermitian vector bundle over M. Suppose D has a self-adjoint extension A in the Hilbert space of…
We show that on groups generated by bounded activity automata, every symmetric, finitely supported probability measure has the Liouville property. More generally we show this for every group of automorphisms of bounded type of a rooted…
We devise an algorithm which, given a bounded automaton A, decides whether the group generated by A is finite. The solution comes from a description of the infinite sequences having an infinite A-orbit using a deterministic finite-state…
The present work determines the exact nature of {\em linear time computable} notions which characterise automatic functions (those whose graphs are recognised by a finite automaton). The paper also determines which type of linear time…
It is consistent (relative to ZFC) that the union of max{b,g} many families in the Baire space which are not finitely dominating is not dominating. In particular, it is consistent that for each nonprincipal ultrafilter U, the cofinality of…
Complex performance measures, beyond the popular measure of accuracy, are increasingly being used in the context of binary classification. These complex performance measures are typically not even decomposable, that is, the loss evaluated…
Countably infinite groups (with a fixed underlying set) constitute a Polish space $G$ with a suitable metric, hence the Baire category theorem holds in $G$. We study isomorphism invariant subsets of $G$, which we call group properties. We…
To each one-dimensional subshift $X$, we may associate a winning shift $W(X)$ which arises from a combinatorial game played on the language of $X$. Previously it has been studied what properties of $X$ does $W(X)$ inherit. For example, $X$…
We investigate properties of ABA+, a formalism that extends the well studied structured argumentation formalism Assumption-Based Argumentation (ABA) with a preference handling mechanism. In particular, we establish desirable properties that…
This paper presents a model of autonomy called autonomy with regard to an attribute applicable to cognitive and not cognitive artificial agents. Three criteria (global / partial, social / nonsocial, absolute / relative) are defined and used…
We give a sufficient geometric condition for a subshift to be measurably isomorphic to a domain exchange and to a translation on a torus. And for an irreducible unit Pisot substitution, we introduce a new topology on the discrete line and…
We consider weighted tree automata over strong bimonoids (for short: wta). A wta $\mathcal{A}$ has the finite-image property if its recognized weighted tree language $[\![\mathcal{A}]\!]$ has finite image; moreover, $\mathcal{A}$ has the…
In 1992, Diestel asked which topological spaces could be represented as the end space of some graph. In 2023, Pitz provided a solution to this question by giving a topological characterization of end spaces using a hereditarily complete…
For bilinear control systems in $\mathbb{R}^d$ we prove, under an accessibility hypothesis, the existence of a nontrivial compact set $D\subset\mathbb{R}^d$ satisfying $\mathcal{O}_t(D)=e^{tR}D$ for all $t>0$, where $R\in\mathbb{R}$ is a…