Computations by fly-automata beyond monadic second-order logic

We present logically based methods for constructing XP and FPT graph algorithms, parametrized by tree-width or clique-width. We will use fly-automata introduced in a previous article. They make possible to check properties that are not monadic second-order expressible because their states may include counters, so that their sets of states may be infinite. We equip these automata with output functions, so that they can compute values associated with terms or graphs. Rather than new algorithmic results we present tools for constructing easily certain dynamic programming algorithms by combining predefined automata for basic functions and properties.Comment: Accepted for publication in Theoretical Computer Scienc

Structural aspects of tilings

In this paper, we study the structure of the set of tilings produced by any given tile-set. For better understanding this structure, we address the set of finite patterns that each tiling contains. This set of patterns can be analyzed in two different contexts: the first one is combinatorial and the other topological. These two approaches have independent merits and, once combined, provide somehow surprising results. The particular case where the set of produced tilings is countable is deeply investigated while we prove that the uncountable case may have a completely different structure. We introduce a pattern preorder and also make use of Cantor-Bendixson rank. Our first main result is that a tile-set that produces only periodic tilings produces only a finite number of them. Our second main result exhibits a tiling with exactly one vector of periodicity in the countable case.Comment: 11 page

On the structure of Ammann A2 tilings

We establish a structure theorem for the family of Ammann A2 tilings of the plane. Using that theorem we show that every Ammann A2 tiling is self-similar in the sense of [B. Solomyak, Nonperiodicity implies unique composition for self-similar translationally finite tilings, Discrete and Computational Geometry 20 (1998) 265-279]. By the same techniques we show that Ammann A2 tilings are not robust in the sense of [B. Durand, A. Romashchenko, A. Shen. Fixed-point tile sets and their applications, Journal of Computer and System Sciences, 78:3 (2012) 731--764]

1D Effectively Closed Subshifts and 2D Tilings

Michael Hochman showed that every 1D effectively closed subshift can be simulated by a 3D subshift of finite type and asked whether the same can be done in 2D. It turned out that the answer is positive and necessary tools were already developed in tilings theory. We discuss two alternative approaches: first, developed by N. Aubrun and M. Sablik, goes back to Leonid Levin; the second one, developed by the authors, goes back to Peter Gacs.Comment: Journ\'ees Automates Cellulaires, Turku : Finland (2010

e-Commerce et logistique urbaine : la consigne automatique, une alternative d'avenir ?

L'essor continu du BtoC fait peser de sérieuses contraintes sur les livraisons urbaines, des livraisons majoritairement réalisées à domicile (LAD). Dans ce contexte, les solutions de livraison hors domicile (LHD) se présentent, de plus en plus, comme des alternatives possibles. C'est la raison pour laquelle notre communication s'y intéresse. Plus précisément, l'objectif de notre recherche est de tenter de cerner les conditions selon lesquelles les réseaux de consignes automatiques (RCA) pourraient devenir une alternative plus performante que la LAD. Après avoir présenté les caractéristiques innovantes de la consigne automatique au regard des autres solutions de LHD, et notamment du point relais, nous proposons une comparaison des réseaux de consignes français, Cityssimo (Groupe La Poste), et allemand, Packstation (DHL). Cette comparaison est effectuée du point de vue de l'offre (conditions techniques d'implantation et de déploiement des réseaux), mais aussi du point de vue de la demande (analyse des comportements des consommateurs) en vue d'apporter quelques explications aux résultats obtenus, résultats qui s'avèrent plutôt contrastés : une apparente timidité du réseau français et un relatif succès de la solution allemande. Un focus est réalisé, à cette fin, sur les comportements des internautes (vis à vis de l'achat à distance et du retrait des colis sans intermédiaire) et sur les conditions techniques de déploiement de ces RCA (différences stratégiques tenant à la position de la consigne automatique au sein des réseaux postaux)

Kolmogorov complexity

The term "complexity" has different meanings in different contexts. Computational complexity measures how much time or space is needed to perform some computational task. On the other hand, the complexity of description (called also Kolmogorov complexity) is the minimal number of information bits needed to define (describe) a given object. It may well happen that a short description requires a lot of time and space to follow it and actually construct the described object. However, when speaking about Kolmogorov complexity, we usually ignore this problem and count only the description bits. As it was common to him, Kolmogorov published, in 1965, a short note that started a new line of research. Aside from the formal definition of complexity, he has also suggested to use this notion in the foundations of probability theory

On the Expressive Power of Quasiperiodic SFT

In this paper we study the shifts, which are the shift-invariant and topologically closed sets of configurations over a finite alphabet in Z^d. The minimal shifts are those shifts in which all configurations contain exactly the same patterns. Two classes of shifts play a prominent role in symbolic dynamics, in language theory and in the theory of computability: the shifts of finite type (obtained by forbidding a finite number of finite patterns) and the effective shifts (obtained by forbidding a computably enumerable set of finite patterns). We prove that every effective minimal shift can be represented as a factor of a projective subdynamics on a minimal shift of finite type in a bigger (by 1) dimension. This result transfers to the class of minimal shifts a theorem by M.Hochman known for the class of all effective shifts and thus answers an open question by E. Jeandel. We prove a similar result for quasiperiodic shifts and also show that there exists a quasiperiodic shift of finite type for which Kolmogorov complexity of all patterns of size ntimes n is Omega(n)