Séries rationnelles
Séries rationnelles à plusieurs variables non commutatives, Hadamard-inversibles
Series which are both max-plus and min-plus rational are unambiguous
Consider partial maps with a rational domain. We show that two families of such series are actually the same: the unambiguous rational series on the one hand, and the max-plus and min-plus rational series on the other hand. The decidability of equality was known to hold in both families with different proofs, so the above unifies the picture. We give an effective procedure...
Series which are both max-plus and min-plus rational are unambiguous
Consider partial maps ∑* → with a rational domain. We show that two families of such series are actually the same: the unambiguous rational series on the one hand, and the max-plus and min-plus rational series on the other hand. The decidability of equality was known to hold in both families with different proofs, so the above unifies the picture. We give an effective procedure to build an unambiguous automaton from a max-plus automaton and a min-plus one that recognize the same series.
Set arithmetic and the enclosing problem in dynamics
We study the enclosing problem for discrete and continuous dynamical systems in the context of computer assisted proofs. We review and compare the existing methods and emphasize the importance of developing a suitable set arithmetic for efficient algorithms solving the enclosing problem.
Set-theoretical operations on -multiple languages
Several comments on pattern recognition system based on the use of attributed grammars
Several methods of the reduction of computational complexity.
Several results on set-valued possibilistic distributions
When proposing and processing uncertainty decision-making algorithms of various kinds and purposes, we more and more often meet probability distributions ascribing non-numerical uncertainty degrees to random events. The reason is that we have to process systems of uncertainties for which the classical conditions like -additivity or linear ordering of values are too restrictive to define sufficiently closely the nature of uncertainty we would like to specify and process. In cases of non-numerical...
Shape Descriptors for Image Analysis
Shape-from-Shading, viscosity solutions and edges.
Shelling hexahedral complexes for mesh generation.
Shift equivalence of P-finite sequences.
Short Note: Counting Conjectures.
Shortest Watchman Routes in Simple Polygons.
Signature verification: A comprehensive study of the hidden signature method
Many handwritten signature verification algorithms have been developed in order to distinguish between genuine signatures and forgeries. An important group of these methods is based on dynamic time warping (DTW). Traditional use of DTW for signature verification consists in forming a misalignment score between the verified signature and a set of template signatures. The right selection of template signatures has a big impact on that verification. In this article, we describe our proposition for...
Signed bits and fast exponentiation
An exact analysis is given of the benefits of using the non-adjacent form representation for integers (rather than the binary representation), when computing powers of elements in a group in which inverting is easy. By counting the number of multiplications for a random exponent requiring a given number of bits in its binary representation, we arrive at a precise version of the known asymptotic result that on average one in three signed bits in the non-adjacent form is non-zero. This shows that...
Signed Chip Firing Games and symmetric Sandpile Models on the cycles
We investigate the Sandpile Model and Chip Firing Game and an extension of these models on cycle graphs. The extended model consists of allowing a negative number of chips at each vertex. We give the characterization of reachable configurations and of fixed points of each model. At the end, we give explicit formula for the number of their fixed points.
Similarity in fuzzy reasoning.
Fuzzy set theory is based on a `fuzzification' of the predicate in (element of), the concept of membership degrees is considered as fundamental. In this paper we elucidate the connection between indistinguishability modelled by fuzzy equivalence relations and fuzzy sets. We show that the indistinguishability inherent to fuzzy sets can be computed and that this indistinguishability cannot be overcome in approximate reasoning. For our investigations we generalize from the unit interval as the basis...
Similarity relations and cover automata
Cover automata for finite languages have been much studied a few years ago. It turns out that a simple mathematical structure, namely similarity relations over a finite set of words, is underlying these studies. In the present work, we investigate in detail for themselves the properties of these relations beyond the scope of finite languages. New results with straightforward proofs are obtained in this generalized framework, and previous results concerning cover automata are obtained as immediate...