Oscillator-Inspired Dynamical Systems to Solve Boolean Satisfiability

• Published in: IEEE journal on exploratory solid-state computational devices and circuits Vol. 9; no. 1; p. 1
• Main Authors: Bashar, Mohammad Khairul, Lin, Zongli, Shukla, Nikhil
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 01.06.2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Boolean Satisfiability; Boolean satisfiability (SAT); Combinatorial analysis; Combinatorial Optimization; Computation; Computational modeling; Dynamical System; Dynamical systems; Mathematical models; Max-NAE-SAT; Max-not-all-equal (NAE)-SAT; Minimization; Optimization; Oscillator; Oscillators; System dynamics
• ISSN: 2329-9231; 2329-9231
• DOI: 10.1109/JXCDC.2023.3241045

Dynamical systems can offer a novel non-Boolean approach to computing. Specifically, the natural minimization of energy in the system is a valuable property for minimizing the objective functions of combinatorial optimization problems, many of which are still challenging to solve using conventional digital solvers. In this work, we design two oscillator-inspired dynamical systems to solve quintessential computationally intractable problems in Boolean satisfiability (SAT). The system dynamics are engineered such that they facilitate solutions to two different flavors of the SAT problem. We formulate the first dynamical system to compute the solution to the 3-SAT problem, while for the second system, we show that its dynamics map to the solution of the Max-NAE-3-SAT problem. Our work advances understanding of how this physics-inspired approach can be used to address challenging problems in computing.