WebRepresenting human and machine computations by discrete dynamical systems, the boundedness and locality conditions can be captured through axioms for Turing computors and Gandy machines; models of these axioms are all reducible to Turing machines. WebThe central and novel aspect of Gandy's formulation lies in the fact that it incorporates parallelism in complete generality. Cellular automata fall directly under Gandy's formulation. And yet, the reduction theorem shows that everything calculable by a device satisfying the constraints, a Gandy machine, is already computable by a Turing machine.

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WebThis can be understood as a Representation Theorem: any particular Gandy machine is computationally equivalent to a two-letter Turing machine, as Turing machines are also Gandy machines. The first fact for Gandy machines, z is determined uniquely up to ∈-isomorphism over x, follows from the next theorem. 45 Before being able to formulate … WebCopeland and Shagrir [14], however, argue that Gandy's principles for mechanisms are not general enough, and instead they present "(ideal) physical machines that lie outside the class of 'Gandy ... WebAug 21, 2000 · Background, Reserv e, and Gandy Machines Andreas Blass 1 , and Y uri Gurevich 2 1 Mathematics Dept., University of Mic higan, Ann Arbor, MI 48109–1109, … red river health and wellness