Related papers: Nonexistence of Minimal Pairs for Generic Computab…
We discuss the ACC conjecture and the LSC conjecture for minimal log discrepancies of generalized pairs. We prove that some known results on these two conjectures for usual pairs are still valid for generalized pairs. We also discuss the…
For any class of operators which transform unary total functions in the set of natural numbers into functions of the same kind, we define what it means for a real function to be uniformly computable or conditionally computable with respect…
We generalize some results on semicomputability by Jockusch \cite{jockusch1968semirecursive} to the setting of $\alpha$-Computability Theory. We define an $\alpha$-Kalimullin pair and show that it is definable in the $\alpha$-enumeration…
A computational abstract machine based on two operations: referencing and bit copying is presented. These operations are sufficient for carrying out any computation. They can be used as the primitives for a Turing-complete programming…
A set $I$ is said to be a universal indifferent set for $1$-genericity if for every $1$-generic $G$ and for all $X \subseteq I$, $G \Delta X$ is also $1$-generic. Miller showed that there is no infinite universal indifferent set for…
This paper argues that the requirement of applicableness of quantum linearity to any physical level from molecules and atoms to the level of macroscopic extensional world, which leads to a main foundational problem in quantum theory…
In parity quantum computing, multi-qubit logical gates are implemented by single-qubit rotations on a suitably encoded state involving auxiliary qubits. Consequently, there is a correspondence between qubit count and the size of the native…
Anyons obtained from a finite gauge theory have a computational power that depends on the symmetry group. The relationship between group structure and computational power is discussed in this paper. In particular, it is shown that anyons…
The purpose of this article is to give, for any commutative ring A, an explicit minimal set of generators for the ring of multisymmetric functions TS^d_A(A[x_1,...,x_r]) as an A-algebra. In characteristic zero, i.e. when A is an algebra…
In this paper, we demonstrate the non-existence of a computational algorithm capable of determining whether the second homotopy group of any compact constructive topological space is trivial. This finding shows the inherent limitations of…
We introduce the notion of finitary computable reducibility on equivalence relations on the natural numbers. This is a weakening of the usual notion of computable reducibility, and we show it to be distinct in several ways. In particular,…
We prove the finiteness of $B$-representations of generalised log canonical pairs. As a consequence, we prove that, the (relative) abundance for a generalised semi-log canonical pair is implied by the abundance for its normalisation.…
While concepts and tools from Theoretical Computer Science are regularly applied to, and significantly support, software development for discrete problems, Numerical Engineering largely employs recipes and methods whose correctness and…
As inductive inference and machine learning methods in computer science see continued success, researchers are aiming to describe ever more complex probabilistic models and inference algorithms. It is natural to ask whether there is a…
In this paper, a simple explanation for the Goldbach Conjecture is given. We have shown that the probability of violating the conjecture not only for the prime numbers, but also for any subset of natural numbers whose distribution is…
It is easy to see that no n-REA set can form a (non-trivial) minimal pair with 0' and only slightly more difficult to observe that no {\omega}-REA set can form a (non-trivial) minimal pair with 0". Shore has asked whether this can be…
For a finite set of non-zero natural numbers that contains at least one element different from 1 and the least common multiple of any of its subsets, there exists a subset of at least half of its members which has a common divisor larger…
Suppose you have an uncomputable set $X$ and you want to find a set $A$, all of whose infinite subsets compute $X$. There are several ways to do this, but all of them seem to produce a set $A$ which is fairly sparse. We show that this is…
This paper provides a new and more direct proof of the assertion that a Turing computable function of the natural numbers is primitive recursive if and only if the time complexity of the corresponding Turing machine is bounded by a…
Partiality is a natural phenomenon in computability that we cannot get around. So, the question is whether we can give the areas where partiality occurs, that is, where non-termination happens, more structure. In this paper we consider…