Jekyll2024-05-24T17:05:30+02:00/semalgo/feed.xmlSéminaire AlgorithmiqueAn amazing seminar.Your NameSous-shifts au langage stable2024-06-18T00:00:00+02:002024-06-18T00:00:00+02:00/semalgo/2024/06/18/talk<p>Les sous-shifts au langage stable forment une classe de sous-shifts qui a été récemment introduite par V. Cyr et B. Kra. Cette famille contient de nombreux exemples classiques de sous-shifts, de diverses complexités allant des systèmes d’entropie strictement positive, comme les sous-shifts de type fini, aux systèmes de faible complexité, comme les sous-shifts de complexité linéaire. Ils sont génériques parmi la famille des sous-shifts. Nous présentons dans cet exposé quelques unes de leurs propriétés, notamment celles concernant les automates cellulaires les préservant.</p>[{"affiliate"=>"LAMFA, Univ. Picardie", "firstname"=>"Samuel", "lastname"=>"Petite"}]Les sous-shifts au langage stable forment une classe de sous-shifts qui a été récemment introduite par V. Cyr et B. Kra. Cette famille contient de nombreux exemples classiques de sous-shifts, de diverses complexités allant des systèmes d’entropie strictement positive, comme les sous-shifts de type fini, aux systèmes de faible complexité, comme les sous-shifts de complexité linéaire. Ils sont génériques parmi la famille des sous-shifts. Nous présentons dans cet exposé quelques unes de leurs propriétés, notamment celles concernant les automates cellulaires les préservant.TBA2024-06-11T00:00:00+02:002024-06-11T00:00:00+02:00/semalgo/2024/06/11/talk<p>TBA</p>[{"affiliate"=>"", "firstname"=>"", "lastname"=>""}]TBATuring machine dynamics and the SMART machine2024-06-04T00:00:00+02:002024-06-04T00:00:00+02:00/semalgo/2024/06/04/talk<p>The study of Turing machines as dynamical systems carried several questions that were not considered before, as the question of the existence of an «aperiodicity», finally solved by the very particular machine called SMART. Combined with other techniques, this machine opened the door for a series of new findings.</p>
<p>In this talk we will recall some of the highlights of this story, but also show some of the remaining open problems, together with some of the attempts to solve them.</p>[{"affiliate"=>"Univ. Conception, Chili", "firstname"=>"Anahi", "lastname"=>"Gajardo"}]The study of Turing machines as dynamical systems carried several questions that were not considered before, as the question of the existence of an «aperiodicity», finally solved by the very particular machine called SMART. Combined with other techniques, this machine opened the door for a series of new findings.Journées du GT SDA2 du GDR IFM à Orléans2024-05-28T00:00:00+02:002024-05-28T00:00:00+02:00/semalgo/2024/05/28/talk[{"affiliate"=>"", "firstname"=>"", "lastname"=>"Pas de séminaire"}]Computability of extender sets in multidimensional subshifts2024-05-21T00:00:00+02:002024-05-21T00:00:00+02:00/semalgo/2024/05/21/talk<p>A classical result from the theory of formal languages, the Myhill-Nerode theorem, gives a necessary and sufficient condition in terms of congruence classes for a language to be regular. In this talk, we try to adapt this result to the case of subshifts, in which we consider potentially multidimensional infinite configurations rather than finite words. In particular, we study the behavior of /extender entropy/, a property introduced by R. Pavlov and T. French which is analogous to congruence classes in formal languages, and obtain some computability characterizations on the possible extender entropies of various classes of subshifts.</p>[{"affiliate"=>"GREYC, Caen", "firstname"=>"Léo", "lastname"=>"Paviet Salomon"}]A classical result from the theory of formal languages, the Myhill-Nerode theorem, gives a necessary and sufficient condition in terms of congruence classes for a language to be regular. In this talk, we try to adapt this result to the case of subshifts, in which we consider potentially multidimensional infinite configurations rather than finite words. In particular, we study the behavior of /extender entropy/, a property introduced by R. Pavlov and T. French which is analogous to congruence classes in formal languages, and obtain some computability characterizations on the possible extender entropies of various classes of subshifts.Synthesis for fragments of first-order logic on data words2024-05-14T00:00:00+02:002024-05-14T00:00:00+02:00/semalgo/2024/05/14/talk<p>History-deterministic automata are intermediary between deterministic and nondeterministic ones, and have been the object of thorough study in the last decade. They offer a way to get a better grasp of the power of nondeterminism, by allowing only some aspects of it: nondeterministic choices are allowed to depend on the past of the computation but not on the future. I will present the state of the art on the understanding of these history-deterministic automata, as well as open problems related to complexity questions. If time permits, I will finish by presenting a recent generalization of history-determinism called explorable automata, where more nondeterminism is allowed, and some intriguing decidability questions remain open.</p>[{"affiliate"=>"LIP, ENS Lyon", "firstname"=>"Denis", "lastname"=>"Kuperberg"}]History-deterministic automata are intermediary between deterministic and nondeterministic ones, and have been the object of thorough study in the last decade. They offer a way to get a better grasp of the power of nondeterminism, by allowing only some aspects of it: nondeterministic choices are allowed to depend on the past of the computation but not on the future. I will present the state of the art on the understanding of these history-deterministic automata, as well as open problems related to complexity questions. If time permits, I will finish by presenting a recent generalization of history-determinism called explorable automata, where more nondeterminism is allowed, and some intriguing decidability questions remain open.Synthesis for fragments of first-order logic on data words2024-05-07T00:00:00+02:002024-05-07T00:00:00+02:00/semalgo/2024/05/07/talk<p>We carry on the study initiated by Bérard et al.[1] of the reactive synthesis problem for distributed systems with an unbounded number of participants interacting with an uncontrollable environment. Executions of those systems are modeled by data words (i.e. finite or infinite words were positions are labeled by an unbounded alphabet), and specifications are given as first-order formulas.</p>
<p>First, we delineate the border between decidability and undecidability for the fragments introduced by Bérard et al.[1]. We then introduce prefix first-order logic, a logic that implements a limited kind of order, and show that this logic has a decidable synthesis problem on data words.</p>
<p>[1] Bérard Béatrice, et al. “Parameterized Synthesis for Fragments of First-Order Logic Over Data Words.” FoSSaCS. 2020.</p>[{"affiliate"=>"LACL, Univ. Paris-Est Créteil", "firstname"=>"Julien", "lastname"=>"Grange"}]We carry on the study initiated by Bérard et al.[1] of the reactive synthesis problem for distributed systems with an unbounded number of participants interacting with an uncontrollable environment. Executions of those systems are modeled by data words (i.e. finite or infinite words were positions are labeled by an unbounded alphabet), and specifications are given as first-order formulas.Domination in subcubic graphs: swapping numbers2024-04-16T00:00:00+02:002024-04-16T00:00:00+02:00/semalgo/2024/04/16/talk<p>In 1996, Bruce Reed worked on domination in cubic graphs, and came to the conclusion that 1/3 of the vertices should suffice in dominating connected cubic graphs. Things are not that simple as there are some counter-examples, but the problem still attracted attention (and gave birth to conjectures). In 2008, Lowenstein and Rautenbach made a relatively short paper (almost 9 pages) proving that the bound holds for graphs with girth 83. After coming back on any graph theoretical concept necessary to understand the proof, I will present how to swap this two numbers, i.e. how to prove that the bound holds for graph of girth 9 in a 83 pages paper…</p>[{"affiliate"=>"GREYC, Caen", "firstname"=>"Paul", "lastname"=>"Dorbec"}]In 1996, Bruce Reed worked on domination in cubic graphs, and came to the conclusion that 1/3 of the vertices should suffice in dominating connected cubic graphs. Things are not that simple as there are some counter-examples, but the problem still attracted attention (and gave birth to conjectures). In 2008, Lowenstein and Rautenbach made a relatively short paper (almost 9 pages) proving that the bound holds for graphs with girth 83. After coming back on any graph theoretical concept necessary to understand the proof, I will present how to swap this two numbers, i.e. how to prove that the bound holds for graph of girth 9 in a 83 pages paper…Développement asymptotique complet pour les systèmes algébriques et au-delà2024-04-09T00:00:00+02:002024-04-09T00:00:00+02:00/semalgo/2024/04/09/talk<p>Nous montrons dans cet exposé comment obtenir de manière algorithmique un développement asymptotique à tous les ordres pour les systèmes algébriques et donnons quelques clefs pour une généralisation pour certains systèmes différentiellement algébriques.</p>[{"affiliate"=>"LIPN, Univ. Paris-Nord", "firstname"=>"Olivier", "lastname"=>"Bodini"}]Nous montrons dans cet exposé comment obtenir de manière algorithmique un développement asymptotique à tous les ordres pour les systèmes algébriques et donnons quelques clefs pour une généralisation pour certains systèmes différentiellement algébriques.How to rotate digital images without losing information?2024-04-02T00:00:00+02:002024-04-02T00:00:00+02:00/semalgo/2024/04/02/talk<p>While rotations are bijections that preserve distances and angles in Euclidean space, these geometric properties are not preserved in general when rotations are applied to digital images. In this talk, we particularlly focus on bijection and topology, which are also generally lost. With regard to bijections, we present the set of rotations that give bijective rotations in \(\mathbb{Z}^2\) and \(\mathbb{Z}^3\). We also show the characterization of such rotations in \(\mathbb{Z}^2\). Turning to topology, we present the class of 2D digital images whose topology is preserved under any rotation, known as (digital) “regular” images, along with “regularization” methods based on an up-sampling strategy. We also show that this notion of regularity cannot be extended to 3D since counter-examples exist.</p>[{"affiliate"=>"GREYC, Caen", "firstname"=>"Yukiko", "lastname"=>"Kenmochi"}]While rotations are bijections that preserve distances and angles in Euclidean space, these geometric properties are not preserved in general when rotations are applied to digital images. In this talk, we particularlly focus on bijection and topology, which are also generally lost. With regard to bijections, we present the set of rotations that give bijective rotations in \(\mathbb{Z}^2\) and \(\mathbb{Z}^3\). We also show the characterization of such rotations in \(\mathbb{Z}^2\). Turning to topology, we present the class of 2D digital images whose topology is preserved under any rotation, known as (digital) “regular” images, along with “regularization” methods based on an up-sampling strategy. We also show that this notion of regularity cannot be extended to 3D since counter-examples exist.