Graph Coloring via Locally-Active Memristor Oscillatory Networks

Abstract

This manuscript provides a comprehensive tutorial on the operating principles of a bio-inspired Cellular Nonlinear Network, leveraging the local activity of NbOx memristors to apply a spike-based computing paradigm, which is expected to deliver such a separation between the steady-state phases of its capacitively-coupled oscillators, relative to a reference cell, as to unveal the classification of the nodes of the associated graphs into the least number of groups, according to the rules of a non-deterministic polynomial-hard combinatorial optimization problem, known as vertex coloring. Besides providing the theoretical foundations of the bio-inspired signal-processing paradigm, implemented by the proposed Memristor Oscillatory Network, and presenting pedagogical examples, illustrating how the phase dynamics of the memristive computing engine enables to solve the graph coloring problem, the paper further presents strategies to compensate for an imbalance in the number of couplings per oscillator, to counteract the intrinsic variability observed in the electrical behaviours of memristor samples from the same batch, and to prevent the impasse appearing when the array attains a steady-state corresponding to a local minimum of the optimization goal. The proposed Memristor Cellular Nonlinear Network, endowed with ad hoc circuitry for the implementation of these control strategies, is found to classify the vertices of a wide set of graphs in a number of color groups lower than the cardinality of the set of colors identified by traditional either software or hardware competitor systems. Given that, under nominal operating conditions, a biological system, such as the brain, is naturally capable to optimise energy consumption in problem-solving activities, the capability of locally-active memristor nanotechnologies to enable the circuit implementation of bio-inspired signal processing paradigms is expected to pave the way toward electronics with higher time and energy efficiency than state-of-the-art purely-CMOS hardware.

A Phase Model of the Bio-Inspired NbOx Local Active Memristor under Weak Coupling Conditions

“…According to the literature [ 49 ], the physical memristor of Figure 1 a can be the equivalent to the structure in Figure 1 b. An intrinsic memristor is connected in parallel with a nonlinear resistor and then it is connected in series with the contact resistor , where the intrinsic memristor’s equation is as follows: where is the equivalent heat capacity, and is the equivalent thermal conductivity of the intrinsic Memristor , respectively; is the ambient temperature.…”

“…According to the literature [49], the physical memristor of Figure 1a can be the equivalent to the structure in Figure 1b. An intrinsic memristor M is connected in parallel with a nonlinear resistor R and then it is connected in series with the contact resistor R C , where the intrinsic memristor's equation is as follows:…”

A Memristor Neural Network Based on Simple Logarithmic-Sigmoidal Transfer Function with MOS Transistors

“…Some valuable properties of memristors are their low energy usage, very good switching and memory properties, high switching speed, nano-sizes, and good compatibility with the present day Complementary MOS (CMOS) integrated chips and circuits [27,28]. Memristors are potentially applicable in memory matrices, reconfigurable analog and digital circuits, neural nets, and many others [29,30]. They are related to storage and computing in a single electronic circuit element [31].…”

Initial state‐dependent implementation of logic gates with memristive neurons

“…The memristor emerges as a promising element for efficiently introducing both memory and non‐linearity into circuits. Demonstrated in previous works [6, 7], memristive dynamics offer energy‐ and time‐efficient solutions in circuit design. This study delves into a fundamental problem from a similar perspective, exploring the potential of leveraging memristive elements for efficient and effective circuit design.…”