research topics:

(under construction)


New

  • A special issue of the International Journal of Foundations of Computer Science on Frontier between Decidability and Undecidability and Related Problems

    Now

    1. Turing machines
      • non-erasing deterministic machines
      • self-describing machines
      • descriptive study of the motion of the machine head on its tape

    2. molecular computing
    3. hyperbolic tilings
    4. cellular automata in hyperbolic geometry
      • the pentagrid of the hyperbolic plane
        JUCS, 5,9 , JUCS, 6,12, TCS site
        technical report, ps file
      • the rectangular dodecahedral tiling of the hyperbolic 3D space
        paper in Fundamenta Informaticae, 58 ,
        technical report, ps file
      • NEW! A book:
        Cellular Automata in Hyperbolic spaces, vol. 1: Theory, Old City Publishing, Philadelphia, 422p.,
        available here, with the possibility to order
        and also here, with another possibility to order
        also available on amazon.fr and on amazon.com
      • a NEW result:
        the injectivity of the global function of a cellular automaton on the ternary heptagrid is undecidable: see arXiv, paper arXiv:0806.1602v2, or/and an abridged version, see here for a .pdf file of it
      • Universality results:
        weak universality results (infinite initial configuration, but a regular one), using the railway circuit model devised by Ian Stewart, see Scientific American, (1994), 90-92.
        • In the pentagrid: a long time ago, with Francine Hermann, 22 states, Theoretical Computer Science 296, (2003), 327-364.
          recently, with Yu Song: 9 states, Parallel Processing Letters, 19(2), (2009), 225-246.
        • In the heptagrid: recently, with Yu Song: 6 states, Electronic Notes in Theoretical Computer Science, 223,(2008), 167-185.
      • Simulations by hyperbolic cellular automata on a triangular grid
        See the slides here.

    Once upon a time

    1. à la Markov constructive analysis
    2. a simple extension of the predicate calculus
    3. practical numbers

    list of publications


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