相关论文: Constructive Algebraic Topology
Computational reflection allows us to turn verified decision procedures into efficient automated reasoning tools in proof assistants. The typical applications of such methodology include mathematical structures that have decidable theory…
Let $X$ be a locally compact Hausdorff space with $n$ proper continuous self maps $\tau_i:X \to X$ for $1 \le i \le n$. To this we associate two topological conjugacy algebras which emerge as the natural candidates for the universal algebra…
computable functions are defined by abstract finite deterministic algorithms on many-sorted algebras. We show that there exist finite universal algebraic specifications that specify uniquely (up to isomorphism) (i) all abstract computable…
Algebraic Combinatorics originated in Algebra and Representation Theory, studying their discrete objects and integral quantities via combinatorial methods which have since developed independent and self-contained lives and brought us some…
A family of algebraic surfaces with many nondegenerate real singularities is introduced with the help of a construction, which has been used in previous works for the generation of substitution tilings.
An algorithm is presented that generates sets of size equal to the degree of a given variety defined by a homogeneous ideal. This algorithm suggests a versatile framework to study various problems in combinatorial algebraic geometry and…
Studies of issues related to computability and computational complexity involve the use of a model of computation. Pivotal to such a model are the computational processes considered. Processes of this kind can be described using an…
Implicit computational complexity, which aims at characterizing complexity classes by machine-independent means, has traditionally been based, on the one hand, on programs and deductive formalisms for free algebras, and on the other hand on…
Realization by linear vector fields is constructed for any Lie algebra which admits a biorthogonal system and for its any suitable representation. The embedding into Lie algebras of linear vector fields is analogous to the classical…
In a previous paper, a process algebra based on ACP (Algebra of Communicating Processes) was proposed in which processes involving data can be handled by means of features originating from imperative programming. In this paper, an extension…
As dynamic and control systems become more complex, relying purely on numerical computations for systems analysis and design might become extremely expensive or totally infeasible. Computer algebra can act as an enabler for analysis and…
Using some new logarithmic formal calculus, we construct a well known vertex algebra, obtaining the Jacobi identity directly, in an essentially self-contained treatment.
Convergence spaces are a generalization of topological spaces. The category of convergence spaces is well-suited for Algebraic Topology, one of the reasons is the existence of exponential objects provided by continuous convergence. In this…
We say that a set is exhaustible if it admits algorithmic universal quantification for continuous predicates in finite time, and searchable if there is an algorithm that, given any continuous predicate, either selects an element for which…
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…
Round-based models are very common message-passing models; combinatorial topology applied to distributed computing provides sweeping results like general lower bounds. We combine both to study the computability of k-set agreement. Among all…
Many combinatorial optimisation problems hide algebraic structures that, once exposed, shrink the search space and improve the chance of finding the global optimal solution. We present a general framework that (i) identifies algebraic…
The topological properties of a set have a strong impact on its computability properties. A striking illustration of this idea is given by spheres and closed manifolds: if a set $X$ is homeomorphic to a sphere or a closed manifold, then any…
We construct a topology on a given algebraically closed field with a distinguished subfield which is also algebraically closed. This topology is finer than Zariski topology and it captures the sets definable in the pair of algebraically…
Semigroups generated by topological operations such as closure, interior or boundary are considered. It is noted that some of these semigroups are in general finite and noncommutative. The problem is formulated whether they are always…