Memcomputing represents a novel form of neuro-oriented signal processing that uses the memristor as a key element. In this chapter, a memristive grid is developed in order to achieve the specific task of solving mazes. This is done by resorting to the dynamic behavior of the memristance in order to find the shortest path that determines trajectory from entrance to exit. The structure of the maze is mapped onto the memristive grid, which is formed by memristors that are defined by fully analytical charge-controlled functions. The dependance on the electric charge permits to analyze the variation of the branch memristance of the grid as a function of time. As a result of the dynamic behavior of the developed memristor model, the shortest path is formed by those memristive branches exhibiting the fastest memristance change. Special attention is given to achieve a realistic implementation of the fuses of the grid, which are formed by an anti-series connection of memristors and CMOS circuitry. HSPICE is used in combination with MATLAB to establish the simulation flow of the memristive grid. Besides, the memristor model is recast in VERILOG-A, a high-level hardware description language for analog circuits
