1,494 research outputs found
Extending the Calculus of Constructions with Tarski's fix-point theorem
We propose to use Tarski's least fixpoint theorem as a basis to define
recursive functions in the calculus of inductive constructions. This widens the
class of functions that can be modeled in type-theory based theorem proving
tool to potentially non-terminating functions. This is only possible if we
extend the logical framework by adding the axioms that correspond to classical
logic. We claim that the extended framework makes it possible to reason about
terminating and non-terminating computations and we show that common facilities
of the calculus of inductive construction, like program extraction can be
extended to also handle the new functions
Inductive and Coinductive Components of Corecursive Functions in Coq
In Constructive Type Theory, recursive and corecursive definitions are
subject to syntactic restrictions which guarantee termination for recursive
functions and productivity for corecursive functions. However, many terminating
and productive functions do not pass the syntactic tests. Bove proposed in her
thesis an elegant reformulation of the method of accessibility predicates that
widens the range of terminative recursive functions formalisable in
Constructive Type Theory. In this paper, we pursue the same goal for productive
corecursive functions. Notably, our method of formalisation of coinductive
definitions of productive functions in Coq requires not only the use of ad-hoc
predicates, but also a systematic algorithm that separates the inductive and
coinductive parts of functions.Comment: Dans Coalgebraic Methods in Computer Science (2008
Robust Mobile Object Tracking Based on Multiple Feature Similarity and Trajectory Filtering
This paper presents a new algorithm to track mobile objects in different
scene conditions. The main idea of the proposed tracker includes estimation,
multi-features similarity measures and trajectory filtering. A feature set
(distance, area, shape ratio, color histogram) is defined for each tracked
object to search for the best matching object. Its best matching object and its
state estimated by the Kalman filter are combined to update position and size
of the tracked object. However, the mobile object trajectories are usually
fragmented because of occlusions and misdetections. Therefore, we also propose
a trajectory filtering, named global tracker, aims at removing the noisy
trajectories and fusing the fragmented trajectories belonging to a same mobile
object. The method has been tested with five videos of different scene
conditions. Three of them are provided by the ETISEO benchmarking project
(http://www-sop.inria.fr/orion/ETISEO) in which the proposed tracker
performance has been compared with other seven tracking algorithms. The
advantages of our approach over the existing state of the art ones are: (i) no
prior knowledge information is required (e.g. no calibration and no contextual
models are needed), (ii) the tracker is more reliable by combining multiple
feature similarities, (iii) the tracker can perform in different scene
conditions: single/several mobile objects, weak/strong illumination,
indoor/outdoor scenes, (iv) a trajectory filtering is defined and applied to
improve the tracker performance, (v) the tracker performance outperforms many
algorithms of the state of the art
The union of unit balls has quadratic complexity, even if they all contain the origin
We provide a lower bound construction showing that the union of unit balls in
three-dimensional space has quadratic complexity, even if they all contain the
origin. This settles a conjecture of Sharir.Comment: 5 pages, 5 figure
Improved Incremental Randomized Delaunay Triangulation
We propose a new data structure to compute the Delaunay triangulation of a
set of points in the plane. It combines good worst case complexity, fast
behavior on real data, and small memory occupation.
The location structure is organized into several levels. The lowest level
just consists of the triangulation, then each level contains the triangulation
of a small sample of the levels below. Point location is done by marching in a
triangulation to determine the nearest neighbor of the query at that level,
then the march restarts from that neighbor at the level below. Using a small
sample (3%) allows a small memory occupation; the march and the use of the
nearest neighbor to change levels quickly locate the query.Comment: 19 pages, 7 figures Proc. 14th Annu. ACM Sympos. Comput. Geom.,
106--115, 199
Continued Fraction Expansion of Real Roots of Polynomial Systems
We present a new algorithm for isolating the real roots of a system of
multivariate polynomials, given in the monomial basis. It is inspired by
existing subdivision methods in the Bernstein basis; it can be seen as
generalization of the univariate continued fraction algorithm or alternatively
as a fully analog of Bernstein subdivision in the monomial basis. The
representation of the subdivided domains is done through homographies, which
allows us to use only integer arithmetic and to treat efficiently unbounded
regions. We use univariate bounding functions, projection and preconditionning
techniques to reduce the domain of search. The resulting boxes have optimized
rational coordinates, corresponding to the first terms of the continued
fraction expansion of the real roots. An extension of Vincent's theorem to
multivariate polynomials is proved and used for the termination of the
algorithm. New complexity bounds are provided for a simplified version of the
algorithm. Examples computed with a preliminary C++ implementation illustrate
the approach.Comment: 10 page
Triangulating the Real Projective Plane
We consider the problem of computing a triangulation of the real projective
plane P2, given a finite point set S={p1, p2,..., pn} as input. We prove that a
triangulation of P2 always exists if at least six points in S are in general
position, i.e., no three of them are collinear. We also design an algorithm for
triangulating P2 if this necessary condition holds. As far as we know, this is
the first computational result on the real projective plane
Concrete Domains
This paper introduces the theory of a particular kind of computation domains
called concrete domains. The purpose of this theory is to find a satisfactory
framework for the notions of coroutine computation and sequentiality of evaluation
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