Massively Parallel Analog Computing: Ariadne’s Thread Was Made of Memristors

This paper explores memristive grids where emergent computation arises through collective device interactions. Computing efficiency of the grids is studied in several scenarios and new composite memristive structures are utilized in shortest path and maze-solving computations. The dependence of the computing medium behavior on the symmetry of both the underlying geometry and the employed devices, is validated through SPICE-level circuit simulations, which highlight important computing inefficiencies. Particular circuit-models of memristive connections enable precise mapping of the target application on the computing medium. Extraordinary functionalities emerge when novel memristive computing components, comprising different electrical characteristics from their structural elements, are introduced in the grid. Applying assisted-computation, by incorporating the concept of Ariadne's thread, leaded to better computing results, which could find application in routing and path computing problems.