MemComputing: An efficient topological computing paradigm

Memcomputing is a novel computing paradigm we have introduced that employs memory (time non-locality) to both store and process information on the same physical location. Memory may be due to any physical property of the system, whether spin, charge or atomic configuration. Digital, hence scalable, memcomputing machines can be designed to solve complex problems very efficiently both in hardware and in software. We will introduce their mathematical definition and provide several examples of complex problems solved using self-organizing logic gates, namely logic gates that organize dynamically to satisfy their logical propositions. We will also show that the power of these machines originates from topological features, instantons, that connect critical points in the phase space with different indexes. Having a topological character, digital memcomputing machines are robust against noise and disorder.