Memcomputing: computing with and in memory using collective states

Massimiliano Di Ventra

Department of Physics, University of California San Diego, La Jolla, CA 92093-0319 USA

Wed, Mar. 25th 2015, 11:15-12:00

SPEC Salle Itzykson, Bât.774, Orme des Merisiers

I will discuss a novel computing paradigm we named *memcomputing* [1] inspired by the operation of our own brain which uses (passive) memory circuit elements or memelements [2] as the main tools of operation. I will first introduce the notion of *universal memcomputing machines* (UMMs) as a class of general-purpose computing machines based on systems with memory. We have shown [3] 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. It is the presence of collective states in UMMs that allows them to solve NP-complete problems in polynomial time using polynomial resources [3]. As an example I will show the polynomial-time solution of the subset-sum problem implemented in a simple hardware architecture that uses standard microelectronic components [4]. Even though we have not proved NP=P within the Turing paradigm, the practical implementation of these UMMs would represent a paradigm shift from present von Neumann architectures bringing us closer to brain-like neural computation [5].

[1] M. Di Ventra and Y.V. Pershin, **Computing: the Parallel Approach,** *Nature Physics*, **9**, 200 (2013).

[2] M. Di Ventra, Y.V. Pershin, and L.O. Chua, **Circuit Elements with Memory:** **Memristors, Memcapacitors, and Meminductors**, *Proc. IEEE*, **97**, 1717 (2009).

[3] F. L. Traversa and M. Di Ventra, **Universal Memcomputing Machines**, *IEEE Transactions on Neural Networks and Learning Systems*, 99 (2015), DOI: 10.1109/TNNLS.2015.2391182.

[4] F. L. Traversa, C. Ramella, F. Bonani, and M. Di Ventra, **Memcomputing NP-complete problems in polynomial time using polynomial resources and collective states**, arXiv:1411.4798

[5] F. L. Traversa, F. Bonani, Y.V. Pershin and M. Di Ventra*, ***Dynamic Computing Random Access Memory**, *Nanotechnology ***25**, 285201 (2014).

Contact : Preden
Roulleau