Posts classified under: Amacc

Cet exposé se situe dans le cadre de la combinatoire des chemins sur réseau. On introduit ici une généralisation des chemins de Dyck (dits “avec trous d’air”), avant de se pencher sur diverses questions classiques à leur sujet : énumération, distributions de motifs, étude de sous-ensembles, etc. Ce faisant, des suites d’entiers positifs (connues dans … Continue reading Séminaire Algorithmique : « Combinatoire énumérative et bijective de différentes familles de chemins de Dyck avec trous d’air », Rémi Maréchal (GREYC, Caen)

En 2023 Smith, Myers, Kaplan et Goodman-Strauss ont découvert le chapeau : une monotuile apériodique du plan euclidien. C’est-à-dire que l’on peut paver le plan euclidien avec des copies (à isométrie près) du chapeau, mais qu’il est impossible de faire un pavage périodique. Simultanément, Greenfeld et Tao ont prouvé l’existence d’un groupe finiment présenté (Z2×H où H est … Continue reading Séminaire Algorithmique : « Un cafard sous le chapeau », Victor Luftalla (LIS, Univ. Aix-Marseille)

The topological properties of a set have a strong impact on its computability properties. A striking illustration of this idea is given by spheres, closed manifolds and finite graphs without endpoints: if a set X is homeomorphic to a sphere, a closed manifold or such a graph, then any algorithm that semicomputes X in some … Continue reading Séminaire Algorithmique : Djamel Eddine Amir (LISN, Univ. Paris-Saclay) « Computability of Compact Spaces »

Several connexions between information theory and combinatorics of graphs have been explored in the last decades. Following this path, we use tools from spectral graph theory to show impossibility results in information theoretic cryptography. We place ourselves in the Kolmogorov complexity framework. After a short introduction to algorithmic information theory and secret key agreement, we … Continue reading Séminaire Algorithmique : Geoffroy Caillat-Grenier (LIRMM, Univ. Montpellier), « From combinatorics of graphs to communication complexity in algorithmic information theory »

Hybrid automata form an expressive model to describe systems combining continuous and discrete evolution modes. However, most verification problems are undecidable for this model. We recall the particular case of Timed Automata where the reachability problem is PSPACE-complete. We introduce the class of Interrupt Timed Automata featuring special clocks called stopwatches that can be suspended. … Continue reading Séminaire algorithmique : Béatrice Bérard (LIP6, Sorbonne Univ.), « The reachability problem for Polynomial Interrupt Timed Automata»

Enumerating is the task of generating all solutions associated with an instance of a computational problem. We refine the complexity landscape for enumeration problems by introducing very low classes defined by using Boolean circuits as enumerators. We locate well-known enumeration problems, e.g., from graph theory, Gray code enumeration, and propositional satisfiability in our classes. In … Continue reading Séminaire Algorithmique : « Enumeration Classes Defined by Circuits », Arnaud Durand (IMJ, Univ. Paris-Diderot)

Balanced binary search trees are a common data structure for implementing ordered sets, with three kinds of queries: checking whether a given value belongs to the set, inserting a value, and deleting a value; the two latter queries require updating the data structure. Some implementations, like red-black trees or weak AVL trees, allow efficient update … Continue reading Séminaire algorithmique : Vincent Jugé (LIGM, Univ. G. Eiffel, Paris Est), « Write-efficient updates for AVL trees »

Coalition formation is a cooperative game theory framework in which a set of agents, required to perform implicit or explicit tasks, must be divided into subgroups (called coalitions), according to collective criteria and a utility function describing the utility of each coalition. This is equivalent to a problem of partitioning the set of agents. The … Continue reading Séminaire Algorithmique : Josselin Guéneron (GREYC) « Repeated Stochastic Coalition Formation: representations and algorithmic approaches »

In 1964, R. Berger proved the existence of strongly aperiodic subshifts of finite type (SFT) on $\mathbb{Z}^2$, and used them to prove the undecidability of the Domino Problem. With the goal of understanding what aspects of $\mathbb{Z}^2$ account for this result, there has been an effort in recent years to characterize the groups with undecidable … Continue reading Séminaire Algorithmique : Nicolas Bitar (LAMFA, Univ. Picardie), « Subshifts of finite type and quasi-isometries beyond groups »