2026-07-17 –, Executive Conference Room
This talk aims at comparing two different approaches to analog computation, the BSS approach and computable analysis, with respect to the condition of locality that expresses the effectiveness of computation. It can be defined for machine-based digital models of computation, such as the Turing machine, by a restriction on the transition function stating that the number of cells the head can move to compute the next state is finite. A refinement of the definition of locality emerges when we compare its formulation in the two accounts of analog models of computation computing in continuous time. The limitation of the former definition comes from the presupposition of the discreteness of symbolic computation. This however isn’t a presupposed property for physical models of computation computing over the reals. Our claim is that locality relies on the finiteness of the representation of the information, relative to the specific manipulation of the reals, referring to exact values or by approximation. Thus if locality participates in the understanding of computation as executed in a step-wise fashion, can it play a similar role for analog models of computation computing in continuous time where information is continuously variable and the finiteness of information not presupposed ?
