A novel memristor-based circuit-level cellular automata (CA)-inspired approach to the solution of the classic sorting problem of n Keys in a linear array is presented. The presented system utilises the structural simplicity of CA combined with the threshold-type switching behaviour of memristors and composite memristive components; the latter is used for both information encoding and computation. The focus is on a threshold-type model for memristors for the implementation of the fundamental CA cell and the overall CA operation is verified via simulations.Introduction: Since the dawn of computing, the sorting problem has been one of the most extensively researched subjects [1]. The main purpose of sorting information is to optimise its usefulness for specific tasks that require sorted input data. Sorting networks, which use comparators built of a series of reciprocally placed memristors, were previously studied in [2]. Memristors (concatenation of 'memory resistors') constitute a recently discovered class of two-terminal passive non-volatile resistance-switching devices which have so far shown abilities that could revolutionise hardware (HW) computing architectures [3][4][5][6][7]. However, the aforementioned network-based HW approach has the following disadvantages, which render its practical use questionable: (i) the comparators' output levels gradually degrade through cascading, thus signal rectification is occasionally required and (ii) the complexity of interconnections increases significantly as the size of the problem (the number of inputs) increases.This Letter addresses the classic sorting problem of n values (Keys) in a linear array by proposing a novel memristor-based circuit-level parallel approach inspired by one-dimensional (1D) cellular automata (CA) [8]. CA constitute a well-studied, inherently parallel, efficient and robust computing paradigm [9]. Owing to their ability to capture globally emerging behaviour from the local collective interaction of simple components, CA have been successfully applied to several computational problems [8][9][10]. Indeed, when CA-based algorithms are implemented in HW they are executed fast by exploiting the parallel structure of CA; HW design reduces to the design of a single CA cell, whereas the overall layout results regular with local interconnections. Here, we present the design of the fundamental memristive CA cell that implements the CA update rule which we employed in the creation of a 1D computational structure, which executes parallel sorting of input Keys. Within the cells, information is encoded in the resistive states of threshold-type switching memristors and composite memristive components. Compared with [2], the proposed design combines the computational capabilities and the size-independent simple structure of CA with the unique circuit properties of memristors, to provide a HW capable of executing computations within memory: