Related papers: The Block Relation in Computable Linear Orders
A pattern of a sequence is a sequence of integer indices with each index describing the order of first occurrence of the respective symbol in the original sequence. In a recent paper, tight general bounds on the block entropy of patterns of…
The objective of this research paper is to study the relationship between a block of a finite group and a defect group of such block. We define a new notion which is called a strongly $k(D)$-block and give a necessary and sufficient…
In this paper, the class of all linearly ordered topological spaces (LOTS) quasi-ordered by the embeddability relation is investigated. In ZFC it is proved that for countable LOTS this quasi-order has both a maximal (universal) element and…
We study a new notion of reduction between structures called enumerable functors related to the recently investigated notion of computable functors. Our main result shows that enumerable functors and effective interpretability with the…
The optimal calculation order of a computational graph can be represented by a set of algebraic expressions. Computational graph and algebraic expression both have close relations and significant differences, this paper looks into these…
Linear-constraint loops are programs whose transition relation is specified by a system of linear inequalities. The termination problem asks, given a loop, whether it admits an infinite computation. Decidability of termination remains open…
Modern experimental methods enable the creation of self-assembly building blocks with tunable interactions, but optimally exploiting this tunability for the self-assembly of desired structures remains an important challenge. Many studies of…
A problem is a multivalued function from a set of \emph{instances} to a set of \emph{solutions}. We consider only instances and solutions coded by sets of integers. A problem admits preservation of some computability-theoretic weakness…
The notion of computability closure has been introduced for proving the termination of the combination of higher-order rewriting and beta-reduction. It is also used for strengthening the higher-order recursive path ordering. In the present…
We present a concept of uniform encodability of theories and develop tools related to this concept. As an application we obtain general undecidability results which are uniform for large families of structures. In the way, we define…
In several classes of countable structures it is known that every hyperarithmetic structure has a computable presentation up to bi-embeddability. In this article we investigate the complexity of embeddings between bi-embeddable structures…
An equivalence structure is a set with a single binary relation, satisfying sentences stating that the relation is an equivalence relation. A computable structure A is said to be $\Delta^0_\alpha$ categorical if for any computable structure…
The paper considers computable Folner sequences in computably enumerable amenable groups. We extend some basic results of M. Cavaleri on existence of such sequences to the case of groups where finite generation is not assumed. We also…
A cohesive power of a computable structure is an effective ultrapower where a cohesive set acts as an ultrafilter. Let $\omega$, $\zeta$, and $\eta$ denote the respective order-types of the natural numbers, the integers, and the rationals.…
It is argued that transformation processes (generation rules) showing evidence of a long evolutionary history in universal computing systems can be generalized. The explicit function class $ \Omega $ is defined as follows: "Operators whose…
Many quantum algorithms for numerical linear algebra assume black-box access to a block-encoding of the matrix of interest, which is a strong assumption when the matrix is not sparse. Kernel matrices, which arise from discretizing a kernel…
Let $S$ be a finitely generated abelian semigroup of invertible linear operators on a finite dimensional real or complex vector space $V$. We show that every coarsely dense orbit of $S$ is actually dense in $V$. More generally, if the orbit…
Nominal Logic is a version of first-order logic with equality, name-binding, renaming via name-swapping and freshness of names. Contrarily to higher-order logic, bindable names, called atoms, and instantiable variables are considered as…
A real number is called left-computable if there exists a computable increasing sequence of rational numbers converging to it. In this article we are investigating a proper subset of the left-computable numbers. We say that a real number…
We consider the posets of equivalence relations on finite sets under the standard embedding ordering and under the consecutive embedding ordering. In the latter case, the relations are also assumed to have an underlying linear order, which…