Universal Memcomputing Machines.

We introduce the notion of universal memcomputing machines (UMMs): a class of brain-inspired general-purpose computing machines based on systems with memory, whereby processing and storing of information occur on the same physical location. We analytically prove that the memory properties of UMMs endow them with universal computing power (they are Turing-complete), intrinsic parallelism, functional polymorphism, and information overhead, namely, their collective states can support exponential data compression directly in memory. We also demonstrate that a UMM has the same computational power as a nondeterministic Turing machine, namely, it can solve nondeterministic polynomial (NP)-complete problems in polynomial time. However, by virtue of its information overhead, a UMM needs only an amount of memory cells (memprocessors) that grows polynomially with the problem size. As an example, we provide the polynomial-time solution of the subset-sum problem and a simple hardware implementation of the same. Even though these results do not prove the statement NP = P within the Turing paradigm, the practical realization of these UMMs would represent a paradigm shift from the present von Neumann architectures, bringing us closer to brain-like neural computation.