Computing systems have seen tremendous growth over the past few decades in their capabilities, efficiency, and deployment use cases. This growth has been driven by progress in lithography techniques, improvement in synthesis tools, architectures and power management. However, there is a growing disparity between computing power and the demands on modern computing systems. The standard Von-Neuman architecture has separate data storage and data processing locations. Therefore, it suffers from a memory-processor communication bottleneck, which is commonly referred to as the \u27memory wall\u27. The relatively slower progress in memory technology compared with processing units has continued to exacerbate the memory wall problem. As feature sizes in the CMOS logic family reduce further, quantum tunneling effects are becoming more prominent. Simultaneously, chip transistor density is already so high that all transistors cannot be powered up at the same time without violating temperature constraints, a phenomenon characterized as dark-silicon. Coupled with this, there is also an increase in leakage currents with smaller feature sizes, resulting in a breakdown of \u27Dennard\u27s\u27 scaling. All these challenges cannot be met without fundamental changes in current computing paradigms. One viable solution is in-memory computing, where computing and storage are performed alongside each other. A number of emerging memory fabrics such as ReRAMS, STT-RAMs, and PCM RAMs are capable of performing logic in-memory. ReRAMs possess high storage density, have extremely low power consumption and a low cost of fabrication. These advantages are due to the simple nature of its basic constituting elements which allow nano-scale fabrication. We use flow-based computing on ReRAM crossbars for computing that exploits natural sneak paths in those crossbars. Another concurrent development in computing is the maturation of domains that are error resilient while being highly data and power intensive. These include machine learning, pattern recognition, computer vision, image processing, and networking, etc. This shift in the nature of computing workloads has given weight to the idea of approximate computing , in which device efficiency is improved by sacrificing tolerable amounts of accuracy in computation. We present a mathematically rigorous foundation for the synthesis of approximate logic and its mapping to ReRAM crossbars using search based and graphical methods
