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Cet article donne les principales caractéristiques de l’école constructive d’Andrej Andreevich Markov (1903–1979). Après un bref rappel de la situation des mathématiques et de la logique au début du xxe siècle, on évoque rapidement la naissance de l’intuitionnisme et de la théorie des fonctions récursives. On décrit ensuite les objets et les méthodes du constructivisme de Markov. A titre d’exemples on expose les principaux résultats relatifs à l’analyse réelle selon le point de vue de Markov. On...
This paper is a contribution to the general tiling problem for the hyperbolic plane.
It is an intermediary result between the result obtained by R. Robinson [
(1978) 259–264]
and the conjecture that the problem is undecidable.
We define a kind of cellular automaton called a hexagonal partitioned
cellular automaton (HPCA), and study logical universality of
a reversible HPCA.
We give a specific 64-state reversible HPCA
, and
show that a Fredkin gate can be embedded in this cellular space.
Since a Fredkin gate is known to be a universal logic element,
logical universality of
is concluded.
Although the number of states of
is greater than those
of the previous models...
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