Binary Matrices under the Microscope: A Tomographical Problem

A binary matrix can be scanned by moving a fixed rectangular window (submatrix) across it, rather like examining it closely under a microscope. With each viewing, a convenient measurement is the number of 1s visible in the window, which might be thought of as the luminosity of the window. The rectangular scan of the binary matrix is then the collection of these luminosities presented in matrix form. We show that, at least in the technical case of a smooth m x n binary matrix, it canbe reconstructed from its rectangular scan in polynomial time in the parameters m and n, where the degree of the polynomial depends on the size of the window of inspection. For an arbitrary binary matrix, we then extend this result by determining the entries in its rectangular scan that preclude the smoothness of the matrix.Comment: 25 pages, 15 figures, submitte

Metric interpretations of infinite trees and semantics of non deterministic recursive programs

AbstractIn order to define semantics of non deterministic recursive programs we are led to consider infinite computations and to replace the structure of cpo on computation domain by the structure of complete metric space. In this setting we prove the two main theorems of semantics: 1.(i) equivalence between operational and denotational semantics, where this last one is defined2.as a greatest fixed point for inclusion,3.(ii) the one-many function computed by a program is the image of the set of trees computed by4.the scheme associated with it

Évaluation des stocks d’investissements directs dans des sociétés non cotées en valeur de marché : méthodes et résultats pour la France.

Depuis 2009, l’estimation des stocks d’investissements directs étrangers en valeur de marché est fondée sur une nouvelle méthode. Sa mise en oeuvre a conduit à une révision substantielle de la position extérieure nette de la France en investissements directs, qui reste néanmoins créditrice à hauteur de 10 % du PIB.Valeur de marché, investissements directs, IDE, groupe international, balance des paiements, position extérieure.

Monoid automata for displacement context-free languages

In 2007 Kambites presented an algebraic interpretation of Chomsky-Schutzenberger theorem for context-free languages. We give an interpretation of the corresponding theorem for the class of displacement context-free languages which are equivalent to well-nested multiple context-free languages. We also obtain a characterization of k-displacement context-free languages in terms of monoid automata and show how such automata can be simulated on two stacks. We introduce the simultaneous two-stack automata and compare different variants of its definition. All the definitions considered are shown to be equivalent basing on the geometric interpretation of memory operations of these automata.Comment: Revised version for ESSLLI Student Session 2013 selected paper

Modularity of Convergence and Strong Convergence in Infinitary Rewriting

Properties of Term Rewriting Systems are called modular iff they are preserved under (and reflected by) disjoint union, i.e. when combining two Term Rewriting Systems with disjoint signatures. Convergence is the property of Infinitary Term Rewriting Systems that all reduction sequences converge to a limit. Strong Convergence requires in addition that redex positions in a reduction sequence move arbitrarily deep. In this paper it is shown that both Convergence and Strong Convergence are modular properties of non-collapsing Infinitary Term Rewriting Systems, provided (for convergence) that the term metrics are granular. This generalises known modularity results beyond metric \infty

Ordered groupoids and the holomorph of an inverse semigroup

We present a construction for the holomorph of an inverse semigroup, derived from the cartesian closed structure of the category of ordered groupoids. We compare the holomorph with the monoid of mappings that preserve the ternary heap operation on an inverse semigroup: for groups these two constructions coincide. We present detailed calculations for semilattices of groups and for the polycyclic monoids.Comment: 16 page

Algebraic Systems and Pushdown Automata

The theory of algebraic power series in noncommuting variables, as we un-derstand it today, was initiated in [2] and developed in its early stages by the French school. The main motivation was the interconnection with context-free grammars: the defining equations were made to correspond to context-fre