We show that the validity of Parikh’s theorem for context-free languages depends only on a few equational properties of least pre-fixed points. Moreover, we exhibit an infinite basis of $\mu$-term equations of continuous commutative idempotent semirings.

We show that the validity of Parikh's theorem for context-free languages depends only on a few equational properties of least pre-fixed points. Moreover, we exhibit an infinite basis of μ-term equations of continuous commutative idempotent semirings.

This paper describes a compact perceptual image model intended for morphological representation of the visual information contained in natural images. We explain why the total variation can be a criterion to split the information between the two main visual structures, which are the sketch and the microtextures. We deduce a morphological decomposition scheme, based on a segmentation where the borders of the regions correspond to the location of the topological singularities of a topographic map. This...

First, a fuzzy system based on ifFirst, a fuzzy system based on if-then rules and with parametric consequences is recalled. Then, it is shown that the globalthen rules and with parametric consequences is recalled. Then, it is shown that the global and local ε-insensitive learning of the above fuzzy system may be presented as a combination of both an ε-insensitive gradient method and solving a system of linear inequalities. Examples are given of using the introduced method to design fuzzy models...

The algebraic counterpart of the Wagner hierarchy consists of a well-founded and decidable classification of finite pointed ω-semigroups of width 2 and height ωω. This paper completes the description of this algebraic hierarchy. We first give a purely algebraic decidability procedure of this partial ordering by introducing a graph representation of finite pointed ω-semigroups allowing to compute their precise Wagner degrees. The Wagner degree of any ω-rational language can therefore be computed...

The algebraic study of formal languages shows that ω-rational sets correspond precisely to the ω-languages recognizable by finite ω-semigroups. Within this framework, we provide a construction of the algebraic counterpart of the Wagner hierarchy. We adopt a hierarchical game approach, by translating the Wadge theory from the ω-rational language to the ω-semigroup context. More precisely, we first show that the Wagner degree is indeed a syntactic invariant. We then define a reduction relation on...

Although the fuzzy retrieval model constitutes a powerful extension of the Boolean one, being able to deal with the imprecision and subjectivity existing in the Information Retrieval process, users are not usually able to express their query requirements in the form of an extended Boolean query including weights. To solve this problem, different tools to assist the user in the query formulation have been proposed. In this paper, the genetic algorithm-programming technique is considered to build...

We propose a concept of decomposable bi-capacities based on an analogous property of decomposable capacities, namely the valuation property. We will show that our approach extends the already existing concepts of decomposable bi-capacities. We briefly discuss additive and $k$-additive bi-capacities based on our definition of decomposability. Finally we provide examples of decomposable bi-capacities in our sense in order to show how they can be constructed.

The aim of this paper is to design a theoretical framework that allows us to perform the computation of regular expression derivatives through a space of generic structures. Thanks to this formalism, the main properties of regular expression derivation, such as the finiteness of the set of derivatives, need only be stated and proved one time, at the top level. Moreover, it is shown how to construct an alternating automaton associated with the derivation of a regular expression in this general framework....

We investigate the extremal function $f(u,n)$ which, for a given finite sequence $u$ over $k$ symbols, is defined as the maximum length $m$ of a sequence $v=a_1{a}_2...a_m$ of integers such that 1) $1\le a_i\le n$, 2) $a_i=a_j,i\ne j$ implies $|i-j|\ge k$ and 3) $v$ contains no subsequence of the type $u$. We prove that $f(u,n)$ is very near to be linear in $n$ for any fixed $u$ of length greater than 4, namely that $$f(u,n)=O\left(n{2}^{O\left(\alpha {\left(n\right)}^{\left|u\right|-4}\right)}\right).$$ Here $\left|u\right|$ is the length of $u$ and $\alpha \left(n\right)$ is the inverse to the Ackermann function and goes to infinity very slowly. This result extends the estimates in [S] and [ASS] which...

Entity and referential integrity are the most fundamental constraints that any relational database should satisfy. We re-examine these fundamental constraints in the context of incomplete relations, which may have null values of the types “value exists but is unknown” and “value does not exist”. We argue that in practice the restrictions that these constraints impose on the occurrences of null values in relations are too strict. We justify a generalisation of the said constraints wherein we use...

Entity and referential integrity are the most fundamental constraints that any relational database should satisfy. We re-examine these fundamental constraints in the context of incomplete relations, which may have null values of the types "value exists but is unknown" and "value does not exist" . We argue that in practice the restrictions that these constraints impose on the occurrences of null values in relations are too strict. We justify a generalisation of the said constraints wherein we use...

In this paper, a family of hybrid control algorithms is presented; where it is merged a free camera-calibration image-based control scheme and a direct force controller, both with the same priority level. The aim of this generalised hybrid controller is to regulate the robot-environment interaction into a two-dimensional task-space. The design of the proposed control structure takes into account most of the dynamic effects present in robot manipulators whose inputs are torque signals. As examples...