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There are 13 equivalence classes of 2D second order quantum and classical superintegrable systems with nontrivial potential, each associated with a quadratic algebra of hidden symmetries. We study the finite and infinite irreducible…
Classical computations can not capture the essence of infinite computations very well. This paper will focus on a class of infinite computations called convergent infinite computations}. A logic for convergent infinite computations is…
We propose cloud oracles, an alternative to machine learning for online optimization of cloud configurations. Our cloud oracle approach guarantees complete accuracy and explainability of decisions for problems that can be formulated as…
This paper shows that, in measurement-based quantum computation, it is possible to write any quantum oracle implementing a classical function in constant depth. The result is shown through the equivalence between MBQC and the circuit model…
In this paper, we investigate finite representations of DatalogMTL models. First, we discuss sufficient conditions for detecting programs that have finite models. Then, we study infinite models that eventually become constant and introduce…
A compact set has computable type if any homeomorphic copy of the set which is semicomputable is actually computable. Miller proved that finite-dimensional spheres have computable type, Iljazovi\'c and other authors established the property…
Infinite time Turing machines (ITTMs) have been introduced by Hamkins and Lewis in their seminal article arXiv:math/9808093. The strength of the model comes from a limit rule which allows the ITTM to compute through ordinal stages. This…
Bennett's notion of depth is usually considered to describe the usefulness and internal organization of the information encoded into an object such as an infinite binary sequence. We consider a natural way to relativize the notion of depth…
A typical oracle problem is finding which software program is installed on a computer, by running the computer and testing its input-output behaviour. The program is randomly chosen from a set of programs known to the problem solver. As…
The partial oracles framework is a quantum search algorithm that has the potential to exceed the quadratic speedup of Grover's algorithm, up to a theoretical maximum of an exponential speedup. Until now, however, the framework has lacked an…
In this paper, we extend Busy Beaver function to a class of higher order Busy Beaver functions based on Turing oracle machine. We prove some results about the relation between decidability of number theoretical formula and higher order Busy…
Functors with an instance of the Traversable type class can be thought of as data structures which permit a traversal of their elements. This has been made precise by the correspondence between traversable functors and finitary containers…
There exists a huge number of numerical methods that iteratively construct approximations to the solution $y(x)$ of an ordinary differential equation (ODE) $y'(x)=f(x,y)$ starting from an initial value $y_0=y(x_0)$ and using a finite…
Missing responses is a missing data format in which outcomes are not always observed. In this work we develop kernel machines that can handle missing responses. First, we propose a kernel machine family that uses mainly the complete cases.…
Kleene's computability theory based on his S1-S9 computation schemes constitutes a model for computing with objects of any finite type and extends Turing's `machine model' which formalises computing with real numbers. A fundamental…
We establish connections between the size of circuits and formulas computing monotone Boolean functions and the size of first-order and nonrecursive Datalog rewritings for conjunctive queries over OWL 2 QL ontologies. We use known lower…
We show that there exists an oracle relative to which quantum commitments exist but no (efficiently verifiable) one-way state generators exist. Both have been widely considered candidates for replacing one-way functions as the minimal…
Ontology-based query answering (OBQA) asks whether a Boolean conjunctive query is satisfied by all models of a logical theory consisting of a relational database paired with an ontology. The introduction of existential rules (i.e., Datalog…
We investigate a variant of the fuel-based approach to modeling diverging computation in type theories and use it to abstractly capture the essence of oracle Turing machines. The resulting objects we call continuous machines. We prove that…
Blind quantum computation is a secure delegated quantum computing protocol where Alice who does not have sufficient quantum technology at her disposal delegates her computation to Bob who has a fully-fledged quantum computer in such a way…