Related papers: A fast coset-translation algorithm for computing t…

We show that an algebra over a cyclic operad supplied with an additional linear algebra datum called Hodge decomposition admits a minimal model whose structure maps are given in terms of summation over trees. This minimal model is unique up…

Let k be a commutative algebra with the field of the rational numbers included in k and let (E,p,i) be a cleft extension of A. We obtain a new mixed complex, simpler than the canonical one, giving the Hochschild and cyclic homologies of E…

Many areas of machine learning and science involve large linear algebra problems, such as eigendecompositions, solving linear systems, computing matrix exponentials, and trace estimation. The matrices involved often have Kronecker,…

We establish upper and lower bounds on the maximal number of steps needed to transform a cyclic permutation to the canonical cyclic permutation using conjugation by adjacent transpositions, and on the diameter of the underlying Schreier…

We introduce an algorithm that conjectures the structure of a permutation class in the form of a disjoint cover of "rules"; similar to generalized grid classes. The cover is usually easily verified by a human and translated into an…

We survey the notion and history of error-correcting codes and the algorithms needed to make them effective in information transmission. We then give some basic as well as more modern constructions of, and algorithms for, error-correcting…

To store and search genomic databases efficiently, researchers have recently started building compressed self-indexes based on grammars. In this paper we show how, given a straight-line program with $r$ rules for a string (S [1..n]) whose…

We present a novel parsing algorithm for all context-free languages, based on computing the relation between configurations and reaching transitions in a recursive transition network. Parsing complexity w.r.t. input length matches the state…

This paper contributes to the mathematical foundations of logic programming by introducing and studying the sequential composition of answer set programs. On the semantic side, we show that the immediate consequence operator of a program…

We revisit Christol's theorem on algebraic power series in positive characteristic and propose yet another proof for it. This new proof combines several ingredients and advantages of existing proofs, which make it very well-suited for…

We present a mathematical framework for mapping second-order logic relations onto a simple state vector algebra. Using this algebra, basic theorems of set theory can be proven in an algorithmic way, hence by an expert system. We illustrate…

The aim of this paper is to present a very simple set of conditions, necessary for the management of knowledge of a poset $T$ of two agents, which are partially ordered by the capabilities available in the system. We build up a formal…

High-throughput computational materials design promises to greatly accelerate the process of discovering new materials and compounds, and of optimizing their properties. The large databases of structures and properties that result from…

The central problem in computational algebraic topology is the computation of the homotopy groups of a given space, represented as a simplicial set. Algorithms have been found which achieve this, but the running times depend on the size of…

We first prove a one-to-one correspondence between finding Hamiltonian cycles in a cubic planar graphs and finding trees with specific properties in dual graphs. Using this information, we construct an exact algorithm for finding…

Partially ordered models of time occur naturally in applications where agents or processes cannot perfectly communicate with each other, and can be traced back to the seminal work of Lamport. In this paper we consider the problem of…

A coreset is a small set that can approximately preserve the structure of the original input data set. Therefore we can run our algorithm on a coreset so as to reduce the total computational complexity. Conventional coreset techniques…

Let $G$ be a finite abelian group $G$ with $N$ elements. In this paper we give a O(N) time algorithm for computing a basis of $G$. Furthermore, we obtain an algorithm for computing a basis from a generating system of $G$ with $M$ elements…

For a (co)monad T_l on a category M, an object X in M, and a functor \Pi: M \to C, there is a (co)simplex Z^*:=\Pi T_l^{* +1} X in C. Our aim is to find criteria for para-(co)cyclicity of Z^*. Construction is built on a distributive law of…

We extend homological perturbation theory to encompass algebraic structures governed by operads and cooperads. The main difficulty is to find a suitable notion of algebra homotopy that generalizes to algebras over operads O. To solve this…