# Formulating Oscillator-Inspired Dynamical Systems to Solve Boolean Satisfiability

arXiv: https://arxiv.org/abs/2209.07571 · HTML: https://mlsanity.com/paper/2209.07571/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Aug 2022.

## Built on by (most cited first, 3 of 3)

- [Higher-Order Kuramoto Oscillator Network for Dense Associative Memory](https://mlsanity.com/paper/2507.21984/) (2025)
- [Oscillators Are All You Need: Irregular Time Series Modelling via Damped Harmonic Oscillators with Closed-Form Solutions](https://mlsanity.com/paper/2602.12139/) (2026)
- [Augmented Electronic Ising Machine as an Effective SAT Solver](https://mlsanity.com/paper/2305.01623/) (2023)

## Abstract (arXiv)

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 formulate 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.