Logic-in-memory (LIM) architectures are explored to address the data transfer bottleneck of conventional von Neumann architectures by integrating computation directly within memory arrays. Among various candidates, memristor-based LIM systems have gained significant attention due to their non-volatile switching behavior and compatibility with dense integration. In this work, a page-wise LIM architecture is implemented using a 3D vertical resistive random-access memory array composed of self-rectifying Pt-Ta₂O₅-Al:HfO₂-TiN memristors. Two logic primitives-1 M and 2 M logic-are employed to perform intra-page and inter-page operations, respectively, enabling core Boolean functions to be executed entirely within the array through resistive state transitions. Based on these logic operations, a memristive arithmetic logic unit (mALU) is designed to perform essential arithmetic functions, including addition, subtraction, increment, and decrement. Owing to the vertical structure of vertical resistive random-access memory, a 2-bit full adder is implemented with a footprint of only three cells and completed in 12 steps. The proposed intra-and inter-page operations, along with complete mALU functionality, are experimentally demonstrated with high reproducibility. Combined with significantly reduced spatiotemporal cost, these results highlight the promise of this architecture for scalable and energy-efficient in-memory computing.

The existing physical implementations of reservoir computing are constrained mainly by time-delay architectures that lack capabilities for spatial data processing. This study presents a multifunctional memristor-based reservoir computing system, the memristive echo state network (MESN), which enables spatiotemporal computation within a single device crossbar array. Utilizing a reconfigurable Ta/HfO₂/RuO₂ memristor, three distinct switching modes are realized: stochastic for input masking, bistable for sigmoidal activation, and analog for precise readout. A full in-memory implementation is experimentally demonstrated using a one-transistor-one-resistor crossbar array integrated with indium oxide thin-film transistors. Spatial inference is validated through cellular automata, confirming reliable hardware operation. High-level simulations based on the hardware results demonstrate the performance of the proposed MESN, achieving high accuracy in predicting the Lorenz attractor and classifying attention-deficit/hyperactivity disorder. The system also predicted the Kuramoto-Sivashinsky equation, representing the first memristor-based reservoir to model complex spatiotemporal partial differential equations. These results highlight the potential of multifunctional memristor arrays for scalable in-memory spatiotemporal computing.