Related papers: Relatively acceptable notation
Any function can be constructed using a hierarchy of simpler functions through compositions. Such a hierarchy can be characterized by a binary rooted tree. Each node of this tree is associated with a function which takes as inputs two…
In this paper we characterize the approximation schemes that satisfy Shapiro's theorem and we use this result for several classical approximation processes. In particular, we study approximation of operators by finite rank operators and…
An automaton is called reachable if every state is reachable from the initial state. This notion has been generalized coalgebraically in two ways: first, via a universal property on pointed coalgebras, namely, that a reachable coalgebra has…
Significant advances in the development of computing devices based on quantum effects and the demonstration of their use to solve various problems have rekindled interest in the nature of the "quantum computational advantage." Although…
Recent studies have shown that the majority of published computational models in systems biology and physiology are not repeatable or reproducible. There are a variety of reasons for this. One of the most likely reasons is that given how…
Tennenbaum's theorem states that the only countable model of Peano arithmetic (PA) with computable arithmetical operations is the standard model of natural numbers. In this paper, we use constructive type theory as a framework to revisit,…
We investigate computability in the lattice of equivalence relations on the natural numbers. We mostly investigate whether the subsets of appropriately defined subrecursive equivalence relations -for example the set of all polynomial-time…
Computably enumerable equivalence relations (ceers) received a lot of attention in the literature. The standard tool to classify ceers is provided by the computable reducibility $\leq_c$. This gives rise to a rich degree-structure. In this…
The physical Church thesis is a thesis about nature that expresses that all that can be computed by a physical system-a machine-is computable in the sense of computability theory. At a first look, this thesis seems contradictory with the…
Experimental science usually relies on laboratory procedures that, after finitely many steps, terminate with numerical reports on physical quantities. This paper argues that such procedures can be understood as algorithmic once the…
A notable feature of the TTE approach to computability is the representation of the argument values and the corresponding function values by means of infinitistic names. Two ways to eliminate the using of such names in certain cases are…
A celebrated result by M. Davis, H. Putnam, J. Robinson, and Y. Matiyasevich shows that a set of integers is listable if and only if it is positive existentially definable in the language of arithmetic. We investigate analogues of this…
A standard tool for classifying the complexity of equivalence relations on $\omega$ is provided by computable reducibility. This reducibility gives rise to a rich degree structure. The paper studies equivalence relations, which induce…
Machine learning models are a powerful theoretical tool for analyzing data from quantum simulators, in which results of experiments are sets of snapshots of many-body states. Recently, they have been successfully applied to distinguish…
We identify a notion of reducibility between predicates, called instance reducibility, which commonly appears in reverse constructive mathematics. The notion can be generally used to compare and classify various principles studied in…
We study the position of the computable setting in the "common theory of locality" developed in arXiv:2106.02066 and arXiv:2204.09329 for local problems on $\Delta$-regular trees, $\Delta \in \omega$. We show that such a problem admits a…
Framed combinatorial topology is a novel theory describing combinatorial phenomena arising at the intersection of stratified topology, singularity theory, and higher algebra. The theory synthesizes elements of classical combinatorial…
We introduce the notion of feedback computable functions from $2^\omega$ to $2^\omega$, extending feedback Turing computation in analogy with the standard notion of computability for functions from $2^\omega$ to $2^\omega$. We then show…
Computational feasibility is a widespread concern that guides the framing and modeling of biological and artificial intelligence. The specification of cognitive system capacities is often shaped by unexamined intuitive assumptions about the…
Literature on Constraint Satisfaction exhibits the definition of several structural properties that can be possessed by CSPs, like (in)consistency, substitutability or interchangeability. Current tools for constraint solving typically…