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Maurice Margenstern

  1. Using Grossone to count the number of elements of infinite sets and the connection with bijections.

    Tue, 06/14/2011 - 15:01 — SomNambul
    Authors: Maurice Margenstern
    Subjects: Discrete Mathematics
    Abstract

    In this paper, we look at how to count the number of elements of a set within
    the frame of Sergeyev's numeral system. We also look at the connection between
    the number of elements of a set and the notion of bijection in this new
    setting. We also show the difference between this new numeral system and the
    results of the traditional naive set theory.

  2. An application of Grossone to the study of a family of tilings of the hyperbolic plane.

    Tue, 06/14/2011 - 15:01 — SomNambul
    Authors: Maurice Margenstern
    Subjects: Discrete Mathematics
    Abstract

    In this paper, we look at the improvement of our knowledge on a family of
    tilings of the hyperbolic plane which is brought in by the use of Sergeyev's
    numeral system based on grossone. It appears that the information we can get by
    using this new numeral system depends on the way we look at the tilings. The
    ways are significantly different but they confirm some results which were
    obtained in the traditional but constructive frame and allow us to obtain an
    additional precision with respect to this information.

  3. An upper bound on the number of states for a strongly universal hyperbolic cellular automaton on the pentagrid.

    Fri, 06/18/2010 - 15:01 — SomNambul
    Authors: Maurice Margenstern
    Subjects: Formal Languages and Automata Theory
    Abstract

    In this paper, following the way opened by a previous paper deposited on
    arXiv, we give an upper bound to the number of states for a hyperbolic cellular
    automaton in the pentagrid. Indeed, we prove that there is a hyperbolic
    cellular automaton which is rotation invariant and whose halting problem is
    undecidable and which has 9~states.

  4. A new weakly universal cellular automaton in the 3D hyperbolic space with two states.

    Thu, 05/27/2010 - 15:01 — SomNambul
    Authors: Maurice Margenstern
    Subjects: Formal Languages and Automata Theory
    Abstract

    In this paper, we show a construction of a weakly universal cellular
    automaton in the 3D hyperbolic space with two states. The cellular automaton is
    rotation invariant and, moreover, based on a new implementation of a railway
    circuit in the dodecagrid,the construction is a truly 3D-one.

  5. About the embedding of one dimensional cellular automata into hyperbolic cellular automata.

    Tue, 04/13/2010 - 15:02 — SomNambul
    Authors: Maurice Margenstern
    Subjects: Formal Languages and Automata Theory
    Abstract

    In this paper, we look at two ways to implement determinisitic one
    dimensional cellular automata into hyperbolic cellular automata in three
    contexts: the pentagrid, the heptagrid and the dodecagrid, these tilings being
    classically denoted by $\{5,4\}$, $\{7,3\}$ and $\{5,3,4\}$ respectively.

  6. Navigation in tilings of the hyperbolic plane and possible applications.

    Mon, 09/14/2009 - 09:02 — SomNambul
    Authors: Maurice Margenstern
    Subjects: Computational Geometry
    Abstract

    This paper introduces a method of navigation in a large family of tilings of
    the hyperbolic plane and looks at the question of possible applications in the
    light of the few ones which were already obtained.

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