We prove that the radix cross-section of a rational set for a length morphism, and more generally for a rational function from a free monoid into N, is rational, a property that does not hold any more if the image of the function is a subset of a free monoid with two or more generators. proceedings short version1 The purpose of this paper is to give a positive answer to a problem left open in a...

Background & objectives: Environmental standards are quantitative criteria for protecting the environment from pollution and degradation. One of the solutions to improve air quality status is to use reasonable limits to prevent excessive release of airborne contaminants from their various sources. On the other hand, these standards are effective in evaluating air pollution reduction strategies....

0.1. Let X be a scheme, reduced and separated, of finite type over Z. For p a prime number, one may consider the set X(Zp) of its Zp-rational points. For every n in N, there is a natural map πn : X(Zp)→ X(Z/p) assigning to a Zp-rational point its class modulo p. The image Yn,p of X(Zp) by πn is exactly the set of Z/p-rational points which can be lifted to Zp-rational points. Denote by Nn,p the ...

Based on the Gröbner basis method, we present algorithms for a complete solution to the following problems in the implicitization of a set of rational parametric equations. (1) Find a basis of the implicit prime ideal determined by a set of rational parametric equations. (2) Decide whether the parameters of a set of rational parametric equations are independent. (3) If the parameters of a set o...

This work revisits set reconciliation, the problem of synchronizing two multisets of xedsize values while minimizing transmission complexity. We propose a new number-theoretic reconciliation protocol called Divide and Factor (D&F) that achieves optimal asymptotic transmission complexity as do previously known alternative algorithms. We analyze the computational complexities of various D&F varia...

Many data mining algorithms use privacy preserving set intersection operations. Private set operations have considered semi-honest and malicious adversarial models in cryptographic settings. Protocols in semi-honest model, requiring light computations, provide weak security. Protocols in malicious model guarantee strong security at the price of expensive computations like homomorphic encryption...

A fuzzy bag is a bag in which each occurrence of an element is associated with a grade of membership. This notion can be viewed as a generalization of the concepts of set, fuzzy set and bag. The set of fuzzy integers (Nf ) provides a general characterization in which all these different concepts are treated in a uniform way and can then be composed. In the field of databases, the use of fuzzy b...

In this paper, we study the continuity of rational functions realized by Büchi finite state transducers. It has been shown by Prieur that it can be decided whether such a function is continuous. We prove here that surprisingly, it cannot be decided whether such a function f has at least one point of continuity and that its continuity set C(f) cannot be computed. In the case of a synchronous rat...

Privacy-preserving data mining has been an active research area in recent years due to privacy concerns in many distributed data mining settings. Protocols for privacy-preserving data mining have considered semi-honest, malicious, and covert adversarial models in cryptographic settings, whereby an adversary is assumed to follow, arbitrarily deviate from the protocol, or behaving somewhere in be...