相关论文: Weihrauch Complexity and the Hagen School of Compu…
Quantum computational complexity estimates the difficulty of constructing quantum states from elementary operations, a problem of prime importance for quantum computation. Surprisingly, this quantity can also serve to study a completely…
Conformal Riemann mapping of the unit disk onto a simply-connected domain $W$ is a central object of study in classical Complex Analysis. The first complete proof of the Riemann Mapping Theorem given by P. Koebe in 1912 is constructive, and…
This paper presents categorical formulations of Turing, Medvedev, Muchnik, and Weihrauch reducibilities in Computability Theory, utilizing Lawvere doctrines. While the first notions lend themselves to a smooth categorical presentation,…
In the past three decades, many theoretical measures of complexity have been proposed to help understand complex systems. In this work, for the first time, we place these measures on a level playing field, to explore the qualitative…
Regular and higher regular graded algebras (in simplest case satisfying Von Neumann regularity $\Theta_{1}\Theta_{2}\Theta_{1}=\Theta_{1}$ instead of anticommutativity) are introduced and their properties are studied. They are described in…
The history of data analysis that is addressed here is underpinned by two themes, -- those of tabular data analysis, and the analysis of collected heterogeneous data. "Exploratory data analysis" is taken as the heuristic approach that…
This talk gives an introduction into the subject of Seiberg-Witten curves and their relation to integrable systems. We discuss some motivations and origins of this relation and consider explicit construction of various families of…
Circular (or cyclic) proofs have received increasing attention in recent years, and have been proposed as an alternative setting for studying (co)inductive reasoning. In particular, now several type systems based on circular reasoning have…
We introduce two new operations (compositional products and implication) on Weihrauch degrees, and investigate the overall algebraic structure. The validity of the various distributivity laws is studied and forms the basis for a comparison…
Computability logic (CL) (see http://www.cis.upenn.edu/~giorgi/cl.html) is a recently launched program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth that logic has more traditionally…
The development of computational techniques in the last decade has made possible to attack some classical problems of algebraic geometry. In this survey, we briefly describe some open problems related to algebraic curves which can be…
We characterize Weihrauch reducibility in E-PA$^{\omega}$ + QF-AC$^{0,0}$ and all systems containing it by the provability in a linear variant of the same calculus using modifications of G\"odel's Dialectica interpretation that incorporate…
Technology is currently ubiquitous and is also part of the educational system at all levels. It started with communication technology systems, and later continued with digital competence. Nowadays, although these previous concepts are still…
In quantum chemistry, the price paid by all known efficient model chemistries is either the truncation of the Hilbert space or uncontrolled approximations. Theoretical computer science suggests that these restrictions are not mere…
In the same sense as classical logic is a formal theory of truth, the recently initiated approach called computability logic is a formal theory of computability. It understands (interactive) computational problems as games played by a…
The study of computability has its origin in Hilbert's conference of 1900, where an adjacent question, to the ones he asked, is to give a precise description of the notion of algorithm. In the search for a good definition arose three…
We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…
The century of complexity has come. The face of science has changed. Surprisingly, when we start asking about the essence of these changes and then critically analyse the answers, the result are mostly discouraging. Most of the answers are…
We systematically study the completion of choice problems in the Weihrauch lattice. Choice problems play a pivotal role in Weihrauch complexity. For one, they can be used as landmarks that characterize important equivalences classes in the…
People solve different problems and know that some of them are simple, some are complex and some insoluble. The main goal of this work is to develop a mathematical theory of algorithmic complexity for problems. This theory is aimed at…