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Algorithmic efficiency is essential to reducing energy and time usage for computational problems. Optimizing efficiency is important for tasks involving multiple resources, for example in stochastic calculations where the size of the random…

In this paper, we study the arithmetics of skew polynomial rings over finite fields, mostly from an algorithmic point of view. We give various algorithms for fast multiplication, division and extended Euclidean division. We give a precise…

In this paper we describe an algorithm for implicitizing rational hypersurfaces in case there exists at most a finite number of base points. It is based on a technique exposed in math.AG/0210096, where implicit equations are obtained as…

We give upper and lower bounds for the number of rational points on Prym varieties over finite fields. Moreover, we determine the exact maximum and minimum number of rational points on Prym varieties of dimension 2.

Inspired by previous work of Shoup, Lenstra-De Smit and Couveignes-Lercier, we give fast algorithms to compute in (the first levels of) the ell-adic closure of a finite field. In many cases, our algorithms have quasi-linear complexity.

This paper deals with simultaneously fast and in-place algorithms for formulae where the result has to be linearly accumulated: some output variables are also input variables, linked by a linear dependency. Fundamental examples include the…

Let $n$ be a positive integer, and let $R$ be a (possibly infinite dimensional) finitely presented algebra over a computable field of characteristic zero. We describe an algorithm for deciding (in principle) whether $R$ has at most finitely…

One important factor determining the computational complexity of evaluating a probabilistic network is the cardinality of the state spaces of the nodes. By varying the granularity of the state spaces, one can trade off accuracy in the…

The efficiency of exact subset sum problem algorithms which compute individual subset sums is defined as $e=min(T/z, 1)$, where $z$ is the number of subset sums computed. $e$ is related to these algorithms' computational complexity. This…

We discuss the computational complexity and feasibility properties of scenario based techniques for uncertain optimization programs. We consider different solution alternatives ranging from the standard scenario approach to recursive…

Our goal is to find accurate and efficient algorithms, when they exist, for evaluating rational expressions containing floating point numbers, and for computing matrix factorizations (like LU and the SVD) of matrices with rational…

We develop general methods to obtain fast (polynomial time) estimates of the cardinality of a combinatorially defined set via solving some randomly generated optimization problems on the set. Geometrically, we estimate the cardinality of a…

Randomized higher-order computation can be seen as being captured by a lambda calculus endowed with a single algebraic operation, namely a construct for binary probabilistic choice. What matters about such computations is the probability of…

Let f be a real or complex polynomial. We give an algorithm to compute the set of generalized critical values. The algorithm uses a finite dimensional space of rational arcs along which we can reach all generalized critical values of f.

Probabilistic argumentation allows reasoning about argumentation problems in a way that is well-founded by probability theory. However, in practice, this approach can be severely limited by the fact that probabilities are defined by adding…

We introduce a non-wellfounded proof system for intuitionistic logic extended with inductive and co-inductive definitions, based on a syntax in which fixpoint formulas are annotated with explicit variables for ordinals. We explore the…

This paper describes an algorithm which computes the characteristic polynomial of a matrix over a field within the same asymptotic complexity, up to constant factors, as the multiplication of two square matrices. Previously, this was only…

A new approach to efficient quantum computation with probabilistic gates is proposed and analyzed in both a local and non-local setting. It combines heralded gates previously studied for atom or atom-like qubits with logical encoding from…

Multipoint polynomial evaluation and interpolation are fundamental for modern symbolic and numerical computing. The known algorithms solve both problems over any field of constants in nearly linear arithmetic time, but the cost grows to…

The chief aim of this paper is to describe a procedure which, given a $d$-dimensional absolutely irreducible matrix representation of a finite group over a finite field $\mathbb{E}$, produces an equivalent representation such that all…