相关论文: Showcasing straight-line programs with memory via …

Interested in formalizing the generation of fast running code for linear algebra applications, the authors show how an index-free, calculational approach to matrix algebra can be developed by regarding matrices as morphisms of a category…

Matrix reduction is the standard procedure for computing the persistent homology of a filtered simplicial complex with $m$ simplices. Its output is a particular decomposition of the total boundary matrix, from which the persistence diagrams…

We propose efficient parallel algorithms and implementations on shared memory architectures of LU factorization over a finite field. Compared to the corresponding numerical routines, we have identified three main difficulties specific to…

The row (resp. column) rank profile of a matrix describes the stair-case shape of its row (resp. column) echelon form. We here propose a new matrix invariant, the rank profile matrix, summarizing all information on the row and column rank…

It is shown that a context-free grammar of size $m$ that produces a single string $w$ (such a grammar is also called a string straight-line program) can be transformed in linear time into a context-free grammar for $w$ of size…

Reasoning requires going beyond pattern matching or memorization of solutions to identify and implement "algorithmic procedures" that can be used to deduce answers to hard problems. Doing so requires realizing the most relevant primitives,…

Scientific computing requires handling large linear models, which are often composed of structured matrices. With increasing model size, dense representations quickly become infeasible to compute or store. Matrix-free implementations are…

Statistics and Optimization are foundational to modern Machine Learning. Here, we propose an alternative foundation based on Abstract Algebra, with mathematics that facilitates the analysis of learning. In this approach, the goal of the…

This dissertation focuses on the design and the implementation of domain-specific compilers for linear algebra matrix equations. The development of efficient libraries for such equations, which lie at the heart of most software for…

Classical existence theorems and solution methods for quadratic programming traditionally rely on the analytical properties of real numbers, specifically compactness and completeness. These tools are unavailable in general linearly ordered…

We develop formal foundations for notions and mechanisms needed to support service-oriented computing. Our work builds on recent theoretical advancements in the algebraic structures that capture the way services are orchestrated and in the…

We investigate the use of linear programming tools for solving semidefinite programming relaxations of quadratically constrained quadratic problems. Classes of valid linear inequalities are presented, including sparse PSD cuts, and…

In logic programming, dynamic scheduling refers to a situation where the selection of the atom in each resolution (computation) step is determined at runtime, as opposed to a fixed selection rule such as the left-to-right one of Prolog.…

We consider feasibility of linear integer programs in the context of verification systems such as SMT solvers or theorem provers. Although satisfiability of linear integer programs is decidable, many state-of-the-art solvers neglect…

We state and analyze a generalization of the "truncation trick" suggested by Gourdon and Sebah to improve the performance of power series evaluation by binary splitting. It follows from our analysis that the values of D-finite functions…

We extend the well known characterization of $\vpws$ as the class of polynomials computed by polynomial size arithmetic branching programs to other complexity classes. In order to do so we add additional memory to the computation of…

Completeness of a logic program means that the program produces all the answers required by its specification. The cut is an important construct of programming language Prolog. It prunes part of the search space, this may result in a loss…

The exact complexity of geometric cuts and bisections is the longstanding open problem including even the dimension one. In this paper, we resolve this problem for dimension one (the real line) by designing an exact polynomial time…

Given a straight-line program whose output is a polynomial function of the inputs, we present a new algorithm to compute a concise representation of that unknown function. Our algorithm can handle any case where the unknown function is a…

In this paper, we consider systems of algebraic and non-linear partial differential equations and inequations. We decompose these systems into so-called simple subsystems and thereby partition the set of solutions. For algebraic systems,…