149 research outputs found
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
L’influence des non-résidents sur la création monétaire dans la zone euro.
Les entrées de capitaux liées aux investissements de portefeuille des non-résidents en titres de la zone euro ont contribué pour près de la moitié à l’accélération de l’agrégat M3 entre septembre 2006 et septembre 2007.M3, agrégats monétaires, contreparties de la masse monétaire, créances extérieures nettes, balance de paiements, investissements de portefeuille, institutions financières monétaires.
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
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
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
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