Section: New Results
Models of Computation
Together with Pablo Arrighi (Grenoble), Gilles Dowek has reformulated Gandy's proof of the physical Church-Thesis in the quantum case [11] . Gilles Dowek has proposed the idea that the Galileo thesis could be seen as a consequence of the physical Church-Turing thesis and therefore as a consequence of Gandy's principles [15] . Gilles Dowek has proposed a definition of a notion of non deterministic computation over the real numbers [14] that could be used as a language to describe continuous non deterministic physical phenomena. All this work has then been presented in a tutorial at the conference Language and Automata Theory and Applications [28] .
Together with Pablo Arrighi, Gilles Dowek has investigated further the principle of a finite density of information [38] and in particular the impact of this definition on the notion of a chaotic dynamical system [37] .
Together with Pablo Arrighi, Gilles Dowek has investigated a generalization of the notion of cellular automaton where the principle of a bounded density of information is formulated independently of the geometry of space. This led to the notion of a Causal graph dynamic [12] .
Nachum Dershowitz and Gilles Dowek have shown that extending Turing machines with a two-dimensional tape, made this formalism usable in practice to implement classical algorithms [45] .
Alejandro Díaz-Caro and Gilles Dowek have proposed to take a fresh look
at non deterministic
Together with Giulio Manzonetto (Paris 13) and Michele Pagani (Paris 13),
Alejandro
Díaz-Caro has considered an extension of the call-by-value
Together with Barbara Petit (Sardes), Alejandro Díaz-Caro has considered the non-deterministic extension of the call-by-value lambda calculus, which corresponds to the additive fragment of the linear-algebraic lambda-calculus. They have defined a fine-grained type system, capturing the right linearity present in such formalisms. After proving the subject reduction and the strong normalisation properties, they have proposed a translation of this calculus into the System F with pairs, which corresponds to a non linear fragment of linear logic. The translation provides a deeper understanding of the linearity in this setting [32] .
Together with Pablo Arrighi, Barbara Petit, Pablo Burias (Rosario), Mauro
Jaskelioff (Rosario), and Benoît Valiron (Penn), Alejandro Díaz-Caro has studied
possible typing systems for the full linear-algebraic