Related papers: Galois Theory of Algorithms
Quantum algorithms are demonstrated to outperform classical algorithms for certain problems and thus are promising candidates for efficient information processing. Herein we aim to provide a brief and popular introduction to quantum…
In the preprint we present an outline of the one dimensional version of topological Galois theory. The theory studies topological obstruction to solvability of equations "in finite terms" (i.e. to their solvabilty by radicals, by elementary…
We prove the Galois correspondence between the subgroups of a finite automorphism group G of a simple vertex operator algebra V and the vertex operator subalgebras of V containing the set V^G of G-invariants.
Searching and sorting used as a subroutine in many important algorithms. Quantum algorithm can find a target item in a database faster than any classical algorithm. One can trade accuracy for speed and find a part of the database (a block)…
The Galois lattice is a graphic method of representing knowledge structures. The first basic purpose in this paper is to introduce a new class of Galois lattices, called graded Galois lattices. As a direct result, one can obtain the notion…
In this paper we give a definition of "algorithm," "finite algorithm," "equivalent algorithms," and what it means for a single algorithm to dominate a set of algorithms. We define a derived algorithm which may have a smaller mean execution…
Many algorithms for inserting elements into tableaux are known, starting with the Robinson-Schensted algorithm. Much of those processes can be incorporated into the general framework of Fomin's "growth diagrams". Even for single types of…
Quantum computing is the process of performing calculations using quantum mechanics. This field studies the quantum behavior of certain subatomic particles for subsequent use in performing calculations, as well as for large-scale…
We define tests of boolean functions which distinguish between linear (or quadratic) polynomials, and functions which are very far, in an appropriate sense, from these polynomials. The tests have optimal or nearly optimal trade-offs between…
A proposal of an algebraic model for the relation between a quantum environment and certain classical particle system is given. The quantum environment is described by a category of possible quantum states, the initial particle system is…
The Integral Image algorithm is often applied in tasks that require efficient integration over images, such as object detection. In this paper we discuss theoretical aspects of the algorithm's continuous version. We suggest to define the…
Sorting algorithms are fundamental to computer science, and their correctness criteria are well understood as rearranging elements of a list according to a specified total order on the underlying set of elements. As mathematical functions,…
Let G be a linear algebraic group, not necessarily connected or reductive, over the field of real numbers R. We describe a method, implemented on computer, to find the first Galois cohomology set H^1(R,G). The output is a list of 1-cocycles…
This paper presents a connection between Galois points and rational functions over a finite field with small value sets. This paper proves that the defining polynomial of any plane curve admitting two Galois points is an irreducible…
This paper unites two research lines. The first involves finding categorical models of quantum programming languages and their type systems. The second line concerns the program of quantization of mathematical structures, which amounts to…
We present a family of algorithms for computing the Galois group of a polynomial defined over a $p$-adic field. Apart from the "naive" algorithm, these are the first general algorithms for this task. As an application, we compute the Galois…
In this paper we focus on functions of the form $A^n\rightarrow \mathcal{P}(B)$, for possibly different arbitrary non-empty sets $A$ and $B$, and where $\mathcal{P}(B)$ denotes the set of all subsets of $B$. These mappings are called…
We establish a general framework for reasoning about the relationship between call-by-value and call-by-name. In languages with computational effects, call-by-value and call-by-name executions of programs often have different, but related,…
When are two algorithms the same? How can we be sure a recently proposed algorithm is novel, and not a minor variation on an existing method? In this paper, we present a framework for reasoning about equivalence between a broad class of…
An algebraic model for the relation between a certain classical particle system and the quantum environment is proposed. The quantum environment is described by the category of possible quantum states. The initial particle system is…